1st January – The first Top of the Pops airs on BBC TV.
2nd January The Beatles "I Want to Hold Your Hand" UK No. 1
4th January The Daleks 3: "The Escape"
9th January The Beatles "I Want to Hold Your Hand" UK No. 1
11th January The Daleks 4: "The Ambush"
16th January (2 weeks) The Dave Clark Five "Glad All Over" UK No. 1
18th January The Daleks 5: "The Expedition"
20th January – Eleven men go on trial at Buckinghamshire Assizes in Aylesbury charged in connection with the Great Train Robbery five months ago.
21st January – Government figures show that the average weekly wage is £16.
22nd January – Film Zulu released.
25th January The Daleks 6: "The Ordeal"
30th January (3 weeks) The Searchers "Needles and Pins" UK No. 1
February
1st February The Daleks 7: "The Rescue"
6th February – The British and French governments agree a deal for the construction of a Channel Tunnel. The twin-tunneled rail link is expected to take five years to build.
7th February – The Beatles arrive in the United States and are greeted by thousands of screaming fans at New York's Kennedy Airport.
8th February The Edge of Destruction 1: "The Edge of Destruction"
9th February – Launch of BBC Wales TV.
9th February – The Beatles perform on The Ed Sullivan Show; their appearance breaks US television ratings records.
11th February – Southampton is granted the status of city, the first such designation of the current reign.
15th February The Edge of Destruction 2: "The Brink of Disaster"
16th February Christopher Eccleston born
21st February – £10 banknotes are issued for the first time since the Second World War.
22nd February Marco Polo 1: "The Roof of the World"
27th February (3 weeks) Cilla Black "Anyone Who Had a Heart" UK No. 1
28th February - Peter and Gordon release their first single, "A World Without Love", a Paul McCartney song that McCartney had decided was "not good enough" for The Beatles. The song ultimately tops the charts in both the UK and the USA.
29th February Marco Polo 2: "The Singing Sands"
March
7th March Marco Polo 3: "Five Hundred Eyes"
10th March – The Queen gives birth to her fourth child, a son (Edward, not yet named).
14th March Marco Polo 4: "The Wall of Lies"
19th March (2 weeks) Billy J. Kramer & The Dakotas "Little Children" UK No. 1
Power dispute talks break down and it is feared that supply disruptions will follow industrial action. The government announces plans to build three new towns in South East England to act as overspill for overpopulated London. One of these is centred around the village of Milton Keynes in north Buckinghamshire.
21st March Marco Polo 5: "Rider From Shang-Tu"
"I Love the Little Things", sung by Matt Monro, the UK's entry in the Eurovision Song Contest, finishes in 8th place.
24th March – John Lennon's first book, In His Own Write is published.
26th March – Verdicts are passed on ten men for their role in the Great Train Robbery after one of the longest criminal trials and longest jury retirals in English legal history.
27th March – The Beatles occupy the top six spots on the Australian pop chart.
28th March Marco Polo 6: "Mighty Kublai Khan"
Pirate radio station Radio Caroline begins broadcasting.
Wax likenesses of The Beatles are put on display in London's Madame Tussauds Wax Museum. The Beatles are the first pop stars to be displayed at the museum.
30th March – Violent disturbances between Mods and Rockers at Clacton beach.
31st March – Minister of Labour Joseph Godber appoints Lord Justice Pearson to chair a court of inquiry into the power dispute.
April
1st April – Ministry of Defence takes over the duties of the War Office, Admiralty, and Air Ministry, which cease to exist. The title of Lord High Admiral is re-vested in the Monarch.
2nd April (3 weeks) The Beatles "Can't Buy Me Love" UK No. 1
4th April Marco Polo 7: "Assassin at Peking"
The Beatles occupy all five top positions on Billboard's Hot 100 with their singles "Can't Buy Me Love", "Twist and Shout", "She Loves You", "I Want to Hold Your Hand", and "Please Please Me".
6 April – Associated-Rediffusion changes its name to Rediffusion, London.
6 April – Associated-Rediffusion changes its name to Rediffusion, London.
9th April – Labour wins the first elections to the Greater London Council.
10th April – Runcorn, a small town in north Cheshire, is designated as a new town by Alec Douglas-Home's government. Extensive house building and industrial and commercial developments are predicted to inflate the town's population to around 70,000 by 1981.
11th April The Keys of Marinus 1: "The Sea of Death"
The National Trust reopens the southern section of the Stratford-upon-Avon Canal, the first major restoration of a canal for leisure use.
The Beatles hold 14 positions on the Billboard Hot 100 chart. Previously, the highest number of concurrent singles by one artist on the Hot 100 was nine by Elvis Presley, December 19, 1956.
16th April – The Rolling Stones release their eponymous début album.
Sentence is passed on eleven men for their role in the Great Train Robbery, seven receiving 30 years each.
18th April The Keys of Marinus 2: "The Velvet Web"
Liverpool win the Football League First Division for the sixth time in their history by beating Arsenal 5–0 at Anfield to secure the title. Everton finish 3rd, behind Manchester United. In their penultimate game of the season, Ipswich Town lose 3–1 to Blackburn Rovers, confirming their relegation two years after winning the League championship.
The scheduled opening night of BBC Two, the UK's third television channel, is disrupted by power cuts, and all that can be screened is announcer Gerald Priestland delivering apologies from Alexandra Palace, meaning the first programme shown is Play School the following morning.
21st April – BBC Two begins scheduled broadcasting; its first programme is Play School.
23rd April (2 weeks) Peter & Gordon "A World Without Love" UK No. 1
25th April The Keys of Marinus 3: "The Screaming Jungle"
Following the debut of BBC2, "The Screaming Jungle" was the first Doctor Who episode to be shown on BBC1 (the previous episodes had been screened on BBC-TV, the single channel available)
29th April – All schools in Aberdeen are closed following 136 cases of typhoid being reported.
30th April – Television sets manufactured as of this date are required to receive UHF channels.
May
2nd May The Keys of Marinus 4: "The Snows of Terror"
West Ham United win the FA Cup for the first time in their history, beating Preston North End 3-2 at Wembley Stadium.
The Queen and The Duke of Edinburgh's seven-week-old son is christened Edward Antony Richard Louis – later he is created Earl of Wessex.
In the United States, The Beatles' Second Album climbs to the #1 spot on the LP charts in only its second week of release.
5th May – Granada Television broadcasts the first in what will become a series of documentary interviews, Seven Up! showing the lives of fourteen school children. Subsequent films in the series have seen them interviewed every seven years since.
6th May – Joe Orton's black comedy Entertaining Mr Sloane premieres at the New Arts Theatre in London.
7th May (2 weeks) The Searchers "Don't Throw Your Love Away" UK No. 1
9th May The Keys of Marinus 5: "Sentence of Death"
11th May – Terence Conran opens the first Habitat store on London's Fulham Road.
16th May The Keys of Marinus 6: "The Keys of Marinus"
21st May The Four Pennies "Juliet" UK No. 1
23rd May The Aztecs 1: "The Temple of Evil"
28th May (4 weeks) Cilla Black "You're My World (Il Mio Mondo)" UK No. 1
30th May The Aztecs 2: "The Warriors of Death"
The 26 part documentary series The Great War covering events in World War I begins airing on the BBC.
June
5th June – The Rolling Stones start their first US tour.
6th June The Aztecs 3: "The Bride of Sacrifice"
13th June The Aztecs 4: "The Day of Darkness"
17th June – Moors murders: A missing persons investigation is launched in Fallowfield, Manchester, as police search for twelve-year-old Keith Bennett, who went missing on the previous evening.
20th June The Sensorites 1: "Strangers in Space"
25th June (2 weeks) Roy Orbison "It's Over"
27th June The Sensorites 2: "The Unwilling Warriors"
July
July – Helen Brook sets up the first Brook Advisory Centre offering teenage contraception and sexual health advice.
6th July The Beatles' first film, A Hard Day's Night, is released.
9th July The Animals "House of the Rising Sun" UK No. 1
10th July – More than 300 people are injured in Liverpool when a crowd of some 150,000 people welcome The Beatles back to their home city.
11th July The Sensorites 3: "Hidden Danger"
15th July – The Post Office Tower in London is completed, although it does not begin operation until October 1965.
16th July The Rolling Stones "It's All Over Now" UK No. 1
18th July The Sensorites 4: "A Race Against Death"
23rd July (3 weeks) The Beatles "A Hard Day's Night" UK No. 1
25th July The Sensorites 5: "Kidnap"
28th July – Winston Churchill retires from the House of Commons at the age of 89.
August
1st August The Sensorites 6: "A Desperate Venture" 
4th August - The first portable televisions go on sale.
8th August The Reign of Terror 1: "A Land of Fear"
12th August - Ian Fleming dies
13th August (2 weeks)
Peter Anthony Allen, at Walton Prison in Liverpool, and Gwynne Owen Evans, at Strangeways Prison in Manchester, are hanged for the murder of John Alan Weston 7 April, the last executions to take place in the British Isles.
15th August The Reign of Terror 2: "Guests of Madame Guillotine"
22nd August The Reign of Terror 3: "A Change of Identity"
The first Match of the Day airs on BBC Two television.
27th August (2 weeks) The Honeycombs "Have I the Right?" UK No. 1
29th August The Reign of Terror 4: "The Tyrant of France"
September
4th September – The Forth Road Bridge opens over the Firth of Forth, linking Fife and Edinburgh.
5th September The Reign of Terror 5: "A Bargain of Necessity"
10th September (2 weeks) The Kinks "You Really Got Me" UK No. 1
12th September The Reign of Terror 6: "Prisoners of Conciergerie" [end of Season 1]
14th September – The final edition of the left-wing Daily Herald newspaper is published.
15th September - The Sun newspaper goes into circulation, replacing the Daily Herald.
Sir Alec Douglas-Home calls a general election for 15 October.
17th September - Goldfinger (James Bond)
21st September – Malta obtains independence from the UK.
October
October – Dorothy Crowfoot Hodgkin wins the Nobel Prize in Chemistry (the first British woman to win a Nobel) "for her determinations by X-ray techniques of the structures of important biochemical substances".
8th October (2 weeks) Roy Orbison "Oh, Pretty Woman" UK No. 1
10th October – The 1964 Summer Olympics opening ceremony at Tokyo, Japan, with first time of live Olympic telecast program by geostationary communication satellite.
13th October – Danger Man returns to ITV after being cancelled in 1961.
15th October – The General election is held. The Labour Party defeats the Conservatives. Harold Wilson becomes Britain's first Labour Prime Minister in thirteen years, replacing Alec Douglas-Home, having gained a majority of five seats.
17th October – Harold Wilson's cabinet is announced; it includes James Callaghan, Denis Healey, Barbara Castle and Roy Jenkins. Jim Griffiths becomes the first Secretary of State for Wales.
18th October – Wilson creates the Welsh Office.
22nd October (3 weeks) Sandie Shaw "(There's) Always Something There to Remind Me" UK No. 1
24th October – Northern Rhodesia, a former British protectorate, becomes the independent Republic of Zambia, ending 73 years of British rule.
The Rolling Stones start their second US tour.
25th October – The Rolling Stones perform on The Ed Sullivan Show for the first time.
28th October – The Wednesday Play premieres on BBC1.
31st October SEASON TWO - Planet of Giants 1: "Planet of Giants"
November
2nd November – ITV soap opera Crossroads airs for the first time.
7th November Planet of Giants 2: "Dangerous Journey"
12th November Roy Orbison "Oh, Pretty Woman" UK No. 1
14th November Planet of Giants 3: "Crisis"
19th November (2 weeks) The Supremes "Baby Love" UK No. 1
21st November The Daleks' Invasion of Earth 1: "World's End"
27th November – Power unions announce that they will start balloting for a strike.
28th November The Daleks' Invasion of Earth 2: "The Daleks"
30th November – Power dispute settled and strike action called off.
3rd December The Rolling Stones "Little Red Rooster" UK No. 1
4th December - "The Likely Lads" begins on TV.
5th December The Daleks' Invasion of Earth 3: "Day of Reckoning"
10th December (5 weeks) The Beatles "I Feel Fine" UK No. 1
12th December The Daleks' Invasion of Earth 4: "The End of Tomorrow"
16th December – Government, Trades Union Congress and employers produce a joint Statement of Intent on Productivity, Prices and Incomes.
21st December – MP's vote 355 to 170 for the abolition of the death penalty, with the abolition likely to be confirmed before the end of next year. The death penalty has gradually fallen out of use over the last twenty years, with the two most recent executions having taken place in August this year.
23rd December – Richard Beeching announces his intention to resign as Chairman of the British Railways Board after three-and-a-half years, during which he proposed the closure of many smaller railway lines, eviscerating the UK's rail network and leaving it the embarassment that it is today.
24th December – The Beatles gain the Christmas number one for the second year running with I Feel Fine, which has topped the singles charts for the third week running. The Beatles have now had six number ones in the United Kingdom alone.
26th December The Daleks' Invasion of Earth 6: "Flashpoint"
Moors murders: Police launch a missing persons investigation after ten-year-old Lesley Ann Downey goes missing from a fairground in Ancoats, Manchester.
31st December – Donald Campbell sets the world speed record on water at 276.33 mph on Dumbleyung Lake in Australia.
Novels
Agatha Christie's Miss Marple novel A Caribbean Mystery.
Ian Fleming's James Bond novel You Only Live Twice and his children's novel Chitty Chitty Bang Bang.
William Golding's novel The Spire.
Philip Larkin's poetry collection The Whitsun Weddings.
Ruth Rendell's first novel From Doon with Death.
Births
13 January – Bill Bailey, comedian
16 February – Christopher Eccleston, actor
29 February – James Ogilvy, son of Princess Alexandra, The Honourable Lady Ogilvy and the Sir Angus Ogilvy
10 March – The Prince Edward (now The Earl of Wessex), youngest son of The Queen
11 March – Shane Richie, actor
17 March - Lee Dixon, English footballer
26 March – Martin Donnelly, Northern Irish racecar driver
3 April – Nigel Farage, United Kingdom Independence Party leader and MEP for South East England
18 April – Niall Ferguson, Scottish historian
20 April - Andy Serkis, English actor
25 April – Andy Bell, singer and songwriter (band Erasure)
28 April – Lady Helen Taylor, daughter of The Duke and Duchess of Kent
1 May – Lady Sarah Chatto, daughter of Antony Armstrong-Jones, 1st Earl of Snowdon and Princess Margaret, Countess of Snowdon
24 May – Adrian Moorhouse, swimmer
13 June – Kathy Burke, actress and comedienne
3 July – Joanne Harris, novelist
21 July - Ross Kemp, English actor
22 July – Bonnie Langford, actress and entertainer
23 July - Matilda Ziegler, actress
19 September - Simon Singh, author
3 October - Clive Owen, English actor
7 October - Paul Stewart, English footballer
7 November – Philip Hollobone, British Conservative politician and MP for Kettering
25 December - Gary McAllister, Scottish footballer, football manager and football coach
Deaths
17 January – T.H. White, author (born 1906)
21 March – Nancy Spain (born 1917) and Joan Werner Laurie (born 1920), journalists, in the crash of a light plane near Aintree
9 June – Max Aitken, 1st Baron Beaverbrook, Canadian-British business tycoon, politician and writer (born 1879)
21 July - John White, footballer (born 1937)
12 August – Ian Fleming, author and journalist (born 1908)
18 September – Clive Bell, art critic (born 1881)
1 December – J. B. S. Haldane, geneticist (born 1892)
8 December – Simon Marks, 1st Baron Marks of Broughton, businessman (born 1888)
9 December – Edith Sitwell, poet (born 1887)
24 December – Claudia Jones, black activist (born 1915)