It's the classic politico's pub debate—who could have solved the country's problems if only they'd not made that key strategic slip or, in some tragic cases, lived long enough to get the job?

One popular choice is SDP co-founder Roy Jenkins, the subject of a talk next week at the Prospect office. Buy tickets here for our evening with his biographer John Campbell.

But who else would we like to have seen behind the desk in Number 10? Here's our list of five great Prime Ministers that never were:

John Smith (Labour)

John Smith with promising young Trade and Industry Spokesman Gordon Brown in 1990. © Sean Dempsey/PA Archive/Press Association Images

The 20th anniversary of the death of this reforming Labour Leader has just passed. The Guardianran a piece by Tony Blair's former Director of Political Operations John McTernan to mark the occasion, under the headline "John Smith would have led us to a decent world" (we won't ask what sort of world he thinks his old boss led us to). Most importantly, Smith would have had a better chance than anyone else at containing the separatist feeling in Scotland which now—for better or worse—threatens to throw Westminster into chaos. A lifelong advocate of the Scottish Parliament and opponent of Scottish nationalism, he memorably set out his opposition to the separatists in 1976, saying: “I say it as a Scot myself, representing a Scottish constituency, born and brought up in Scotland, living and wishing to continue living in Scotland, a member of a Scots profession, with children at Scottish schools, and having roots too deep in Scotland ever to wish to sever them. I think I am as entitled as any separatists to speak for my fellow countrymen.”

What kept him from the job? Smith died suddenly aged 55 in 1994. The Sun's front page the next day read: "Britain's next Prime Minister died yesterday."

Rab Butler (Conservative)

Butler speaking at a rally in Blackpool in 1963. He received a standing ovation. © PA/PA Archive/Press Association Images.

Butler's long and distinguished career saw him serve in three of the four "great offices of state," (Chancellor of the Exchequer, Home Secretary and Foreign Secretary) but he was always pipped to the top job. He first made his name as Conservative President of the Board of Education (a position now known as Secretary of State for Education). Sent to a corner of Parliament which then-Prime Minister Winston Churchill saw as a bit of a backwater, Butler made the role his own. He pushed through the 1944 Education Act, which secured free secondary education for all. Later, as Chancellor, he worked on a broadly Keynesian agenda, sticking to his convictions despite criticism from the right of his party.

What kept him from the job? Harold Macmillan once criticised Butler as "a politician of vague ambition." That's a polite way of saying he wasn't good enough at stabbing people in the back. Also, his decision to speak out against military action in Suez in 1956 probably scuppered his standing within the party.

Kenneth Clarke (Conservative)

Kenneth Clarke—everyone's favourite loveable grouch

Many modern politicians have endured searing satirical portraits on TV—Norman Tebbit's Spitting Image puppet for example. So the affection felt for Kenneth Clarke across the political spectrum is demonstrated nowhere more than in political comedy The Thick of It, in which the bumbling but ultimately good-hearted Tory Cabinet Minister Peter Mannion is supposedly based on Clarke. Clarke is the moderate Tory par excellence—pro-Europe and a great media performer. If he'd held the reins of the party in opposition during the last decade, he wouldn't have had to go looking for hoodies to hug—they'd all have wanted to hug him. He's an economic heavyweight too; his work as Chancellor in the early 90s saw interest rates, inflation and unemployment all falling.

What kept him from the job? Clarke has always been too outspoken to make the grade in a party which traditionally relies on its right-wing grassroots. It is tempting to say Clarke, cigar and brandy in hand, would have been more than a match for ale-swilling Nigel Farage, but his cosmopolitan views would be unlikely to wash with Ukippers.

Michael Heseltine (Conservative)

Heseltine swarmed by press during his leadership campaign in 1990. © Nigel Marple/AP/Press Association Images.

Heseltine, nicknamed "Tarzan" in the 80s for his voluminous (and, quite frankly, beautiful) hair, has always been seen as an efficient operator. His experience in business—he founded Haymarket, which owns MediaWeek, Management Today and other titles in the 1950s—has earned him respect within his party. He became the yuppie-ish face of urban regeneration as Thatcher's Environment Secretary, playing a key role in the sale of council houses under right to buy.

What kept him from the job? Heseltine was beaten in a leadership contest in 1990 by future Prime Minister John Major. He could not recover from being smeared as Thatcher's executioner, having played an instrumental role in her downfall, and even those who agreed that the Iron Lady had to be scrapped couldn't quite bring themselves to support the man who did the deed.

Tony Benn (Labour)

Benn with a copy of the Labour Government's white paper on nationalisation in 1974. © PA/PA Archive/Press Association Images.

The late Tony Benn has been called the "Grandfather of British Politics," and was known in his old age as a great speaker and man of morals beloved by both sides of the House. As a young politician, however, he was a firebrand, and in the mid-70s (and later in opposition) was Thatcher and the new right's loudest critic. A Guardian obituary recently argued that his challenges to the government during these years "shattered the centre of British politics." Proudly socialist, Benn refused to take part in the neoliberal "me decade." Lefties mourn his downfall to this day.

What kept him from the job? Benn lost out on the deputy leadership of the party in 1981, and in so doing retired from frontline politics to become one of Westminster's greatest backbench rhetoricians. The battle still rages as to whether Labour's subsequent move to the right was unavoidable, but in the reforms of the Kinnock/Smith/Blair era, Benn began increasingly to look like a man out of time.