It was in late August that David Cameron telephoned the American Republican senator John McCain and invited him to be the star turn at the Conservative party conference. McCain, whom the polls put neck and neck with the Democrat Hillary Clinton as favourite to be the next president of the United States, had met a Conservative delegation earlier in the year. "It was just a general gathering: 'Hi, how are you' - no strategy, no tactics," he says.
When I speak to Senator McCain a month after Cameron's call, he has not yet written his speech, but the themes are likely to be familiar to McCain watchers. He describes himself as a Reaganite, "big tent" conservative. His political positions owe less to party discipline than to private conscience. "I try to do what is right," he says. His votes of conscience have in the past set him against fellow Republicans, George W Bush in particular. The president became increasingly irritated by McCain's mission to reform the financing of political campaigns - particularly as he has done rather well out of big donors. He also resented McCain's support for the Kyoto treaty and his concern for the environment.
More recently, Bush has felt further moral heat from an alliance between the former secretary of state Colin Powell and McCain over the US treatment of prisoners in Guantanamo Bay. McCain is not a team player. When he ran against Bush for the Republican nomination in 2000, Bush supporters accused him of being a closet Democrat. Actually, they accused him of far worse. They put it about that he was mentally unstable after being a prisoner at the notorious "Hanoi Hilton" camp for six years during the Vietnam war, and they whispered that his youngest daughter, adopted from a Bangladeshi orphanage run by Mother Teresa, was actually McCain's biological child by a black prostitute. He was incensed by the dirty tactics, telling Bush he "should be ashamed".
McCain certainly tests the tenets of the religious right. He once described the Pat Robertson Christian Coalition as an "evil influence over the Republican Party". He has taken on the National Rifle Association, demanding background checks on those buying guns. He supports stem-cell research, favours a "don't ask, don't tell" approach to gays in the army and, while describing himself as "pro-life", makes exceptions and suggests that if his daughter became pregnant, it would be her choice whether she kept the baby.
Worst, he is unsound on tax cuts, saying: "Sixty per cent of the benefits from Bush's tax go to the wealthiest 10 per cent of Americans. I'm not giving tax cuts to the rich." Yet his personal approval rating in the United States is consistently high. "Character is the single most important thing in politics," he tells me.
To the young Conservative leader, who beats Gordon Brown on personality in the British polls, this is all welcome. For a start, McCain is in tune with his foreign-policy ideas. According to the historian Niall Ferguson, who advises Cameron on foreign policy and who is also close to the senator, Cameron's recent speech suggesting that America should show a little humility would be endorsed by McCain.
Ferguson has in mind a fond father-son relationship between McCain and Cameron as "character" winners of elections in 2008. "McCain for president, Cameron for prime minister - that is my dream scenario," says Ferguson. McCain may not in the end have the political funds he needs, he may be too old, and he may have offended the Republicans beyond repair, but he is certainly putting everything into his campaign, touring as only he can, paying enormous attention to detail and eclipsing Hillary Clinton in media coverage. (It is still just as likely to be a Hillary Clinton/Gordon Brown partnership, however, with Bill Clinton - whom McCain vigorously opposed in office - happy to endorse the Chancellor as a future prime minister.)
There is a McCain personality cult in America. "John Wayne McCain," people shout at rallies. He is self-deprecating, declining the sobriquet hero, even though he was remarkably brave when tortured at the Hanoi Hilton, refusing to leave Vietnam before his turn, even though his father was a serving admiral. When he finally arrived home on crutches to wife and family, his frightened six-year-old son asked his mother: "But where will he sleep?"
Yet a man who writes a book called Why Cour age Matters and cites Winston Churchill as his hero is not unaware of his public image.
There is a story he tells about a fellow prisoner at the Hanoi camp, who sewed an American flag inside his shirt. When it was discovered, he was beaten until nearly blind, but he returned to his cell, got out his bamboo needle and began making a new flag. Nancy Reagan could not hear of McCain's experiences without her eyes welling with tears. He is hawkish on foreign policy, but speaks as a military man with a father and grandfather who were war heroes, an 18-year-old son, Jimmy, in the marines, and an older son, Jack, at the Naval Academy. Both sons can expect to be sent to Iraq or Afghanistan.
McCain does not know David Cameron well, but tells me he is impressed by him for "the way he has reinvigorated the Conservative Party and the youth movement in a Conservative vision for the future. I admire his enthusiasm and the way he is ubiquitous. It is a wonderful thing to see this youth."
I ask him if, as a presidential candidate turning 70, he minds the cult of youth. "Reagan turned this to an asset," he reminds me.
McCain has also met Gordon Brown. Were he to become president, who would he be more comfortable dealing with - Cameron or Brown? He says tactfully: "Whoever is president of the United States and whoever is the British prime minister, the unique relationship between the countries will remain." But he does also say: "As a conservative Republican, I encourage Republicanism round the globe."
But isn't it the special relationship that is dragging down the present leaders? Iraq is the top issue in the US polls and it has done for Tony Blair. McCain believes both leaders have suffered from the "frustration of voters". "I have different views on some issues, but I view [Blair] with great appreciation," he says. "Our soldiers are fighting side by side and the relationship has never been better."
I suggest he might have more in common with Cameron-style Conservatism than with his native "God and guns" Republicanism, but receive a firm put-down. "The difference is that the Republican Party has been in power for a period, whereas the British Conservatives have been out of power." Nor will he be drawn on whether Cameron has been wise to distance himself from core Con servative principles such as low taxes. He plays the American visitor. Internal feuds are a matter for Britain. He is just an anglophile "student of history". The highlights of his previous visit were to see Churchill's bunker and observe Prime Minister's Questions.
McCain firmly believes in the rightness of the cause in Iraq and Afghanistan, although he has been severely critical of the Donald Rumsfeld strategy, of expecting quick results and shrugging off the consequences of invasion as "stuff". He has demanded that the Bush administration be straight "with the American people about the high costs and many difficulties of the mission".
"Winning over insurgency takes years," the senator tells me.
On Afghanistan, he departs from the formal convention that there is no difference between British and American strategy. McCain says that the biggest threat is narcotic traders taking hold of the south. I counter that the British have de liberately decided to make the eradication of the poppy crop a lower priority than fighting the Taliban. McCain replies sharply that "it is hard to micromanage from here, but the crop this year is at an all-time high. That has implications - and devastating consequences for Europe. We have to act to reduce output."
We have been talking during the anniversary of 9/11, and I ask what progress we have made on the war on terror. Are we safer now than then? He replies: "In the US we have not had an attack after 11 September, though some people thought we would. The president and the administration and intelligence deserve great credit."
Of attacks elsewhere he says: "Life isn't fair."
John McCain will declare that he is running for president early next year. He is emphatic that his decision would not be affected were Condoleezza Rice, the secretary of state, to enter the race (though it would certainly affect his lead in the poll ratings). He stood aside for Bob Dole in 1996; he won't stand aside again. McCain knows that this is his last chance. Naturally, he has the "highest respect" for Rice, just as he judges Hillary Clinton to be "a formidable opponent, whom you underestimate at your peril".
McCain may have curbed his famous temper - he was full of old-world courtesy during our conversation - but he is still tough and determined. As Richard Nixon said of him: "He's scrappy. He's a fighter."
He also has charisma. "He walks into a room and it's 'Bling bling bling' and everybody's sort of dazzled," Ronald Reagan's former campaign assistant Nancy Reynolds says of him.
David Cameron would dearly like to bask in that bling.
1936 Born in the Panama Canal Zone, son and grandson of two prominent naval officers
1958 Graduates from the United States Naval Academy
1967 Shot down in his A-4 Skyhawk in Vietnam and held as a prisoner of war in Hanoi until 1973
1980 Marries second wife, Cindy Hensley McCain (pictured right). They have four children
1982 Stands and wins election to the House of Representatives in Arizona's first congressional district
1986 Replaces retiring Republican senator Barry Goldwater
1997 Time names him one of the 25 most influential Americans
2000 Stands in the Republican presidential primaries. Loses after false claims about his private life
2004 Supports George W Bush in his campaign for re-election