She was 25. He was 77 and treated her with elaborate gallantry. Her first decision was what her surname was (Windsor, rather than Mountbatten); her last of his government was who his successor should be. (Everyone assumed it would be Eden, so she asked him.)
Tricky moment: Should she suggest that Churchill stand down on grounds of illness? (She rather thought she would not.)
Anthony Eden 1955-57
Outwardly dashing and courtly, he turned out to be surprisingly stiff and formal. He was 57 when he finally became prime minister. He had been described as a future prime minister ever since he served as foreign secretary in the 1930s – even longer than Gordon Brown. He was the first divorced PM, which was a big deal then.
Tricky moment: Suez: she knew all about Eden's secret deals but could do nothing about them.
Harold Macmillan 1957-63
She was 30 when another old man – Macmillan was 62 – "emerged" from the aristocratic wing of the Tory party. He pursued a "chivalrous fantasy", according to Ben Pimlott's biography, The Queen. "Supermac" wrote long "obsequious" memos and received "friendly and informal" replies.
Tricky moment: The "wind of change" meant colonies becoming independent, and South Africa leaving the Commonwealth.
Alec Douglas-Home 1963-64
Dry as a matchstick, but with an equally dry wit. He was the closest to the Queen in background, interests and temperament of all her prime ministers. A family friend of the Bowes-Lyonses who renounced his earldom. But he wasn't around long.
Tricky moment: Anthony Blunt, Surveyor of the Queen's Pictures, confessed in 1963 to being the "fourth man" of a Soviet spy ring, which was revealed to the public in 1979.
Harold Wilson 1964-70, 1974-76
She had little in common with the wily socialist. "He behaved towards her – unexpectedly – as an equal," wrote Pimlott. Their ages were closer: he was 48, she was 38. She was "flattered by his eagerness to take her into his confidence", and their audiences grew longer, which was noted with interest by the royal household.
Wilson used life peerages rather than creating new hereditary peers which changed the royal ecosystem.
Tricky moment: Rhodesia declared itself independent in the name of the Queen.
Edward Heath 1970-74
"Gallantry was not Heath's style," said Pimlott. "He could be abrupt to the point of rudeness, and had no small talk." Nor did he see the need to win favour. "She was never comfortable with him," said a former courtier. He had no interest in the Commonwealth and didn't see a role for her in foreign affairs.
Tricky moment: Joining the EEC was a big deal, for a sovereign monarch.
James Callaghan 1976-79
An old guy again: he was 64; she was 49. But he was a devoted monarchist. "Conversation flowed easily, and could roam anywhere," he recalled later. "There was even a flirtatious frisson," Pimlott wrote. "The Prime Minister would compliment the Monarch on her clothes, and she would respond with banter."
Tricky moment: The chaotic life of Princess Margaret, the Queen's sister.
Margaret Thatcher 1979-90
Different deal. Same age (53). In their relations, said Pimlott, "there was a rigidity that never softened". Their audiences "are dreaded by at least one of them", wrote Anthony Sampson in Anatomy of Britain. The Queen's unhappiness with Thatcher's divisive social policies leaked into the daylight.
Tricky moment: When they appeared in public wearing the same colour.
John Major 1990-97
First PM who was younger. She was 64; he was 47. The Queen "discovered in him a more relaxed congenial visitor than his predecessor", according to Pimlott. But they formed no special bond, despite his government and her family being in parallel crises.
Tricky moment: Collapse of marriages of Duke of York and Prince of Wales, the latter in 1992, her annus horribilis.
Tony Blair 1997-2007
Even younger. He was 43. She was in her seventies. Like previous Labour prime ministers, he laid it on thick, so much so that the Queen is believed to think Blair should have been a Tory. She said in 1998: "I believe that there is an air of confidence in this country of ours just now." But the romance soured, not so much because of Cherie's failure to curtsey, but because he was a moderniser who banned fox hunting.
Tricky moment: Anti-monarchical backlash after death of Diana, Princess of Wales.
Gordon Brown 2007-10
Charming and solicitous in private. Almost nothing is known about their relationship. She once asked, "Has the Prime Minister got lost? He disappeared the wrong way at the crucial moment," with an amused air, when he wasn't in his place at a state banquet at Windsor in 2008. And she asked on a visit to a bank, "Why did no one see it coming?" about the financial crisis, but that did not seem to be aimed specifically at Brown.
Tricky moment: It was all tricky, from the election that never was onwards.
David Cameron 2010-
Another 43-year-old, rosy cheeked this time. Dosop (definitely our sort of person), if not quite in the Douglas-Home bracket: his brother used to come to tea at Windsor because he was at prep school with Edward. Got his job at Central Office after a call from someone who worked at the palace. Probably highly attentive, quick and deferential without grovelling in private.
Tricky moment: The forming of the coalition, which might have posed awkward questions about the royal prerogative, but didn't.