leader of the (reduced majority) Labour party.. It's not like the US system where you have an elected President. The UK head of state is actually the monarch. The Prime Minister is just a Member of Parliament who is chosen as the leader by his party - more like a Senate leader or Congress leader, I suppose. Once chosen, he remains leader until there's a challenge (there's no term limit on the leadership of a party). If they want to get rid of him, Labour will have to hold a leadership contest.
He still has a lot of support amongst Labour MPs (astonishingly - shows what slimy toadying politicians they are).
The only hope is that either
1) he becomes so unpopular that the wider Labour party force a leadership contest. Then we probably get Brown, and find out what his foreign policy would look like. Currently little known, since he rarely speaks about it. (He did recently say he would have gone to war in Iraq just like Tony, but that was during an election, and he really had to say it or look like he was knifing Blair in the back.
Or 2) with the parliamentary majority down to about 66, a group of 34 labour MPs could inflict a defeat on the government. And there are around 40-60 who are disenchanted enough to do it. Except that on most votes where they might oppose Blair, probably the Tory party (the 2nd largest) would vote with Blair.
By far the majority of the policies announced after bLiar's recent election win are quite in line with the Thatcherite economic and foreign policies that the Conservatives have been pushing for the last 25 years (not least in their slavish obedience to the US in matters of foreign policy) which shows how far he has taken the party to the right since the days of the 1980's when Labour supported unilateral nuclear disarmament and were broadly antagonistic to US foreign policy.
There's an interesting article about Blair and "New Labour", written around the time when Blair came into power ('97) about how a significant portion of his first cabinet were alumni of a transatlantic project called "BAP" - the British American Project for the Successor Generation, set up during the Reagan years, and funded by some RW org (that I think even had ties to WACL!)
From that perspective, it can look like Blair was set up by the US to change the direction of the Labour party in its favour - a poodle indeed!
The article's at (and please excuse the URL - it's not their article ;-) )
http://www.bilderberg.org/bap.htm#Tom