When news of the handover of authority in Iraq to the new interim government reached him Monday at the NATO summit in Istanbul, President Bush reacted instinctively. He reached out and shook the hand of the man in the next chair, British Prime Minister Tony Blair.

The handshake, replayed frequently on the BBC, symbolized what many Britons, including both supporters and opponents of Blair's government, consider the strangest and most politically provocative personal alliance in the world -- the partnership that has been struck between the Republican president and the Labor prime minister.

No one doubts the depth of their friendship -- not even those among Blair's fellow partisans who despise the solid front they have formed on the war in Iraq.

So closely are Bush and Blair aligned that Bush's fate in the Nov. 2 American election could have an impact on what happens to Blair next May 5, the date most pundits are guessing the next British general election will be held.

There is no way to sugarcoat one fact of political life: Except for those who are very close to Blair and feel constrained to defend his choice of friends, George Bush is scorned here. His poll ratings are low, and much of the public seems to accept the caricature of him as an impulsive gunslinger. At a luncheon of nine or 10 conservative writers, politicians and strategists at the Centre for Policy Studies, a think tank that became influential in Margaret Thatcher's day, the descriptions of Bush began with "recklessly incompetent" and went downhill from there.

A close student of Blair's government says, "No one in the cabinet wants Bush reelected, except perhaps for Blair himself." The prime minister's closest associates are careful about what they say, but one of them concedes that if Bush were gone, it would be much easier to recruit grass-roots volunteers to campaign for Labor candidates next May.

But among Blair's political strategists, it's also recognized that if Bush loses, it probably will be because Iraq has proved to be a foreign policy disaster -- and that same force could threaten Blair. In the spring, when the fighting in Iraq was growing and the prison abuse story threatened to implicate British troops, rumors circulated in Westminster that Blair might be forced by his own backbenchers to resign.

That is no longer the case. He has weathered the crisis, and his party seems ready to fight a third election under his leadership -- even if the assumption is that he would probably step down sometime in the following four years, perhaps after the promised referendum on joining the European Union. He is helped by the fact that the Conservative Party leadership was at least as firmly in support of going to war with Saddam Hussein as Blair was. The Liberal Democrats are the only "peace" party, and they are not strong enough to threaten.

Nonetheless, a palpable tension surrounds the Bush-Blair partnership and the Iraq war they jointly plotted. In a few weeks, Blair will face the report of a blue-ribbon commission investigating the British intelligence failure on weapons of mass destruction and be required, once again, to justify his support for a showdown with Hussein.

"Blair feels that he is on all fours with Bush" in continuing to believe that the world is better off with Hussein in captivity, one senior adviser says. But the price for standing with Bush has been high. Blair's goal of integrating Britain into Europe has been set back by the opposition to his Iraq stance from France, Germany and now Spain. Blair's hopes for progress on a Middle East settlement have been dashed by Bush's embrace of Ariel Sharon's territorial policy. And almost every time Dick Cheney or Don Rumsfeld opens his mouth, Blair's people wince.

But he sticks like glue -- for a complex of personal and political reasons that intrigue observers. Americans can find excellent guides to the dynamics of the relationship in a pair of books by two of the best British political journalists. Peter Riddell of the Times of London has just updated his 2003 paperback, "Hug Them Close." And in September, Public Affairs will publish "The Accidental American" by the BBC's James Naughtie.

Both make the point that Bush is fortunate to have found such a friend in a man whose reputation now stands higher in America than at home. Whether Blair is equally lucky remains to be seen, but he is convinced that nothing could be worse than a U.S. administration left wholly isolated.

davidbroder@washpost.com