Gene Volokh has a post discussing the possibility of "impeaching" Tony Blair. I think this is, at the very least, far-fetched. Unlike in the United States, there is an easy, constitutionally-mainstream, recently-used mechanism for removing a Prime Minister in the UK--removal by his party and replacement by a new leader. While there are surely a few backbench cranks in the Labour Party happy to resurrect a long-unused provision in British constitutional practice in order to get rid of Blair, there is as much chance of this happening as there is of me becoming the King of Sweden.
There is a non-neglible chance that the Labour party will decide to rise up and replace Blair, but I find this unlikely as well. Someone has to throw themselves up as a human sacrifice in order to get the process started, with the knowledge that there is a very small chance that they'll actually get to be Prime Minister. The usual process is that someone of less than top-drawer status challenges the PM, in a vote of the governing party it turns out that there's lots of support for "anyone but the incumbent," thereby inducing the big guns to enter the race, or encourage the sitting PM to step down. If anyone would do this, it'd be Robin Cook, the former Foreign Minister. But the process has additional steps that didn't exist when they purged Maggie Thatcher, that would draw the whole thing out this time. So my best guess is that Blair is safe until the next election. If he's smart, he'll wait for things to die down, for his popularity to tick up a bit, and then step down, saying that he's accomplished most of what he set out to do, made the Labour Party an electorally powerful machine in a way that it never was before him, and open the way for Gordon Brown to become PM. If he can pull this off, the internal strife in the Labour Party disappears and the government goes on to another big win in the next election (which, in my mind, is certain given that a referendum on entering EMU will not occur until after the election is held). So I think all of this is just pundit-fodder.