Mr Profumo and Miss Keeler were from two different worlds. He was part of the inner circle of the British traditional establishment while she was part of the brash, new Britain rapidly taking shape around it.
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They met and began an affair, a liaison which he subsequently denied in Parliament.
Rumours began to circulate that secret information on nuclear weapons could have been passed via Miss Keeler to Captain Ivanov, and Mr Profumo eventually resigned from the government after admitting he had lied to the Commons.
The events stoked huge national interest and Harold Macmillan's government, which was a closed world of public schoolboys, was struggling to make the brave decisions needed to tackle the economic difficulties. Its troubles were lampooned by satirists.
Macmillan resigned and Labour won the general election the following year by four seats.
What happened at and after Cliveden ripped open the whole way of ruling Britain. The secretive establishment cliques were confronted by the impertinent, publicity-crazed, 1960s. And "the chaps" lost.
The Sixties is most remembered, however, as a mythical period of British history.
The country turned from the black and white austerity of the 40s and 50s into a Technicolor, psychedelic Garden of Eden.
A heady optimism was shared by people who had never enjoyed this kind of cultural power before
Not since before the Romans invaded had long-haired people wandered around in public wearing so little.
And not since the early Christians had love been so earnestly declared the answer to almost everything.
A heady optimism was shared by people who had never enjoyed this kind of cultural power before - the children of dockers and factory workers bringing a transfusion of energy that pale, old Britain badly needed.
Harold Wilson, the new prime minister, hailed the dawn of the classless society.
A period which lasted 15 years and began during his premiership saw modern Britain starting to rise.
Cool Britannia, 60s-style
The look and shape of the country which was formed during 1964-79 is still here today, essentially unaltered - the motorways and mass car economy, the concrete architecture, the rock music, the high street chains.
Here "modern" also means a belief in planning and management. This was the time of practical men, educated in grammar schools, sure of their intelligence, rolling up their sleeves and taking no nonsense.
They were going to scrap the old and fusty, whether that meant the huge Victorian railway network, the grand Edwardian palaces of government in Whitehall, regiments, terraced housing, the grim laws of their ancestors - hanging, theatre censorship, the prohibitions on homosexual behaviour and abortion - or the ancient coinage and quaint county names.
Bigger in general would be better. Huge comprehensive schools would be more efficient and fairer than the maze of selective and rubbish-heap academies.
The many hundreds of trade unions would resolve themselves into a few leviathans, known only by their initials.
Small companies would wither and combine and ever-larger corporations would arise in their place, ruthless, sleek and scientifically managed.
1960s - TIME OF SOCIAL CHANGE
The 1960s saw massive shifts in cultural attitudes. In 1961 polite society was shocked by cabinet minister John Profumo's affair.
Eyebrows were raised as hemlines went up. Contraceptives became available, and abortion and homosexuality were legalised.
The formerly rigid social structures began to break down, as 'meritocracy' became a social phenomenon.
Pirate radio forced the authorities to cater for the hunger for pop music. In 1967 the BBC launched Radio One.
And youth had become more politicised - the anti-Vietnam demonstrations in 1968 being just one example.
These were years of increased social mobility, a time of impatience with the old class domination.
The country was full of little Harolds and lesser Teds, bright men and women from lower middle-class or working class families who were rising fast through business, universities and the professions, who hugely admired such leaders.
When Wilson talked of the scientific revolution that would transform Britain, his audience included tens of thousands of managers and engineers, in their off-the-peg tweed jackets and flannel trousers, who shared his vision entirely.
In the early 60s, the wartime generation were still in control of the country.
But a cascade of reforms happened later in the decade, headed by the liberal Home Secretary Roy Jenkins, who detected an appetite for "a more civilised society".
'Rivers of blood'
So divorce became easier, hanging was abolished, homosexuality decriminalised for men over 21 and abortion was legalised.
And the older Britons who grew up in a time characterised by deference and order thought the country was turning into a permissive and irresponsible society.
One thing was certain. Britain was becoming a more divided one, on several fronts.
Mass protests were staged over the Vietnam War, but they failed to persuade Wilson to condemn the country's creditor, the US.
After a slow start, the Mini was a huge hit
And among white Britons there were fears Britain was under siege from Commonwealth immigrants, a feeling stirred up by Tory outsider Enoch Powell in his famous "rivers of blood" speech in 1968.
And the Sixties ended as they began, with protests. There were seven million working days lost to strikes in 1969.
Even the Mini, held up as a triumph for British design, provided a dark warning about the future of British business and manufacturing because it was sold too cheaply.
The optimism of the Sixties was starting to evaporate and it was clear there were tough times ahead.
Andrew Marr's History of Modern Britain continues on BBC Two on Tuesday, 29 May, at 2100 BST.
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