Pleased to meet you, hope you guess my name: The Swinging Sixties' great get-togethers

It was, as they like to say, a fashion moment: when, in 1962, the photographer David Bailey bundled the model Jean Shrimpton on to a plane to New York with orders to provide British Vogue with some pretty spreads. For a few harum-scarum days the pair zipped around the grottier areas of Manhattan. They brought back a fistful of shots of Shrimpton in an amusement park, a street market, stepping in puddles, and pinned by chain-link fences. The few who saw the shoot never forgot it. Was it fashion photography or street photography?

Now, the BBC is to dramatise that episode, and the affair the two initiated, in We'll Take Manhattan, with Aneurin Barnard as Bailey and Karen Gillan as Shrimpton (inset right).

But what other great meetings came to define the ideas, attitudes and mores of the Swinging Sixties? And what legacies remain?

The Beatles meet the Maharishi

August 1967 in the Park Lane Hilton, London

The Fab Four met the Maharishi Mahesh Yogi at the Park Lane Hilton and liked what they heard from the bearded one about transcendental meditation – so much so that they trooped off to Bangor the next day to stay in a hall of residence with several hundred other acolytes for more TM instruction (the same day they learned of the death of Brian Epstein). The following February John, Paul, George and Ringo (with case full of baked beans) found themselves at the Maharishi's place in India wondering if he was quite the guru he proclaimed ...

Legacy: The yet-to-be-proven implication that rock'n'roll is a suitable vehicle for higher thoughts beyond this veil of tears.

See also: Sting, Bono, Cliff Richard

Christine Keeler meets John Profumo

1961 at Cliveden, Buckinghamshire, seat of Lord Astor

The Secretary of State for War and the call girl met – in the presence of Profumo's wife – at a house party, and a brief affair followed. We might not have heard anything of the Tory minister's discreet trysts had it not been for Keeler's chaotic private life, which caught the attention of the press, and out it all came, most importantly her association with a Russian naval attaché. Oops! In 1963 Profumo resigned for lying to the House of Commons, and within a few months the Prime Minister, Harold Macmillan, had also resigned.

Legacy: The last nail in the coffin of deference and the glorious first flush of the political sex scandal.

See also: Cecil Parkinson, Jeffrey Archer, Peter Robinson

Vidal Sassoon meets Mary Quant

1963 in New Bond Street, London

He had the spiffy new haircut; she had the mini-skirt – but Quant was the bigger name when she walked into Sassoon's salon and invited him to try out a cut to adorn the models wearing her next collection. Vidal's big chance! But as he fashioned Quant's hair into his new five-point bob, he nicked the designer's ear with his scissors. No matter, the bob was the job, and became Quant's signature style and, indeed, the look of early Swinging London.

Legacy: Sassoon's bob swept the world, and no wonder – it represented tonsorial emancipation from the bonds of the set and blow dry. No, really, it did.

See also: Jennifer Aniston, Anna Wintour, Boris Johnson

Jimi Hendrix meets Eric Clapton

October 1966 at Regent Street Polytechnic, London

The chance to meet Eric Clapton had been dangled before Jimi Hendrix as he considered a trip to Britain. After a whirlwind couple of weeks in London, he did just that, jamming with Cream. After watching Hendrix tear through a Howlin' Wolf song, "Slowhand" famously exclaimed to Hendrix's manager, Chas Chandler: "You never told me he was that fucking good!"

Legacy: Apart from Clapton's brief wannabe-Jimi perm? The endless look-at-me guitar solo, which is totally awesome/annoying (delete as appropriate).

See also: Jimmy Page, Prince, Brian May

Elizabeth Taylor meets Richard Burton

1961 on the set of the film Cleopatra

It was the affair to end them all: a handsome Welsh womaniser seduces his "home-wrecker" co-star while the two of them act out one of the great love stories in a film production that was burning through cash as quickly as Taylor got through husbands. Oh, and they were both married. Phew! The lovers were papped relentlessly, and the 29-year-old Taylor was accused of "erotic vagrancy" by the Vatican, during what became known as Le Scandale.

Legacy: The celebrity marriage lived out, for ill or good, in magazines, newspapers and websites everywhere.

See also: Charles and Di, Madonna and Sean Penn, Katie and Peter

We'll Take Manhattan, 10.30pm, Thursday, BBC4