It could all have turned out so differently.

According to Secretary of State Rice in “The Blair Decade,” a PBS documentary airing tonight, President Bush was so concerned that British participation in the Iraq war would cost Prime Minister Blair the premiership that he suggested Britain send no troops at all to Iraq. Although Mr. Bush was grateful for such conspicuous support, America did not need the 10,000 personnel Mr. Blair was offering to dispatch to Basra. But the prime minister insisted. He was convinced that Saddam Hussein’s weapons of mass destruction presented an imminent threat to Britain and he wanted to contribute directly to the dictator’s demise.

Mr. Blair, once the most popular prime minister since polls began gambled everything on the war. He spent his immense reserves of cred it with voters, who overwhelmingly doubted the need for Hussein’s re moval, and employed his extraordi nary powers of eloquence and per suasion to convince parliament that if the tyrant was not stopped, the world would soon face a far more terrible threat. It was a fatal miscal culation. Within weeks of the fall of Baghdad, Mr. Blair had to return to his ultimate masters in the House of Commons and concede that no WMDs had been found. Americans were aghast when they watched as Prime Minister Thatcher was made to walk the plank by her own party in 1990 Next month, Mr. Blair, too, will be defenestrated, the victim of a palace coup orchestrated by his erstwhile friend Gordon Brown

The British system of government is far less forgiving than the American division of powers. Were America a parliamentary democracy, Mr. Bush would be long gone. “The Blair Decade,” an entertaining and engrossing British-made documentary, offers a sophisticated account of Mr. Blair’s rise and fall, and, though it contains few surprises to those who follow British politics, it explains why it was not just Mr. Blair’s devotion to Mr. Bush’s Iraq plan that caused his ouster. Like Ms. Thatcher before him, Mr. Blair was elected to improve his nation’s public services but soon found it more exciting to stride the world stage, teaming up with his soul mate, President Clinton, to save the people of Kosovo from Slobodan Milosevic’s genocidal attacks. Like Ms. Thatcher and the Falklands, having tasted the delights of a successful foreign adventure, Mr. Blair was hooked.

He was able to largely ignore the home front by forging a pact with Mr. Brown, his formidable chancellor, that echoed the wartime deal struck between Winston Churchill and Clement Attlee, in which Churchill managed military strategy and divvied up the world with President Franklin Roosevelt and Joseph Stalin while his Labour counterpart was given free rein to start building the welfare state. It was only when the Iraq war went cruelly wrong that Mr. Blair resumed his interest in the more mundane matters of education, social services, and health, by which time it was too late.

In the meantime, Mr. Brown had transformed Britain into the booming economic capital of Europe. Not even Ms. Thatcher’s chancellors were able to maintain such a steady increase in the country’s wealth, in large part because Mr. Brown defied Mr. Blair’s wishes and kept Britain out of the euro zone. At one stage, the film suggests, Mr. Blair offered Mr. Brown carte blanche to run the whole government, if only the chancellor would agree to dump the pound in favor of the euro. Mr. Brown would not be tempted, and on June 27, he will inherit the premiership that for many years he has believed is rightfully his.

The Blair-Brown rivalry forms the centerpiece of “The Blair Decade.” Like Tudor contenders for the throne, the two have laced their once fast friendship with duplicity, plotting, obfuscation, and treachery. The taciturn Mr. Brown brooded on when to invoke the pact by which Mr. Blair agreed to take the premiership in turns. Like Ms. Thatcher, Mr. Blair failed to read the signs that he was terminally wounded and had become an electoral liability. His alliance with Mr. Bush took an enormous toll on his popularity, and by repeatedly putting off the handover to Mr. Brown, he may well have cost Labour the next election.

Ms. Thatcher’s mentor, Enoch Powell, once said that all political lives end in failure; right now it would seem that Mr. Blair’s reputation is at rock bottom. But these are early days. By learning the lessons of Ms. Thatcher’s proscriptions and building upon her legacy, Mr. Blair transformed Labour’s fortunes. He led the party to three consecutive victories, beating four different Tory leaders — a record challenged only by Prime Minister Harold Wilson, who won four elections out of five. He stripped the party of its last vestiges of confiscatory socialism and encouraged its members to enjoy the widespread prosperity that only a market economy can provide. Iraq, which undid his winning streak, remains a work in progress.

Aged just 54, the same age that Mr. Clinton ceased being president, Mr. Blair has at least one more substantial job before him. What he chooses to do will likely be the key to whether we remember him fondly or as a British electoral curiosity.