The British
do hate this war in Iraq and generally always have. More importantly to Blair is that the Labour Party has lost a lot of support due to the war and he is likely very concerned that Gordon Brown (his handpicked successor) may not be able to retain the post after he leaves.
It has nothing to do with Prince Harry and in general the royals aren't much of a concern for British MP's unless you're of a particular faction of the Conservative Party known as the "flag and family" group of whom there just aren't very many.
the British people haven't supported the war since the get go, if you hadn't noticed
I have no idea where you get your information Sirs, but it confirms to me that you really don't know much about the world beyond the U.S.
According to MORI (IPSOS MORI is a respected polling firm in Britain) the beginning of the war had a 23% approval rating. By 2005 support was hovering around 30 to 35%.
The majority of British citizens didn't believe that Saddam Hussein should have received the death penalty. I think your perception of Britain is way off.
This also has to be quite expensive for them.
I think the real issue is political. Tony Blair is a political mastermind. Probably one of the best politicians of modern times in both Britain and the United States. I'd place him up there with Clement Atlee, Pierre Trudeau, and Bill Clinton. Perhaps more intelligent than all three. You can bet that he's looked at this from every angle and it has little or nothing to do with the "job being done" (mind you Prime Minister Blair also said "the invasion has been a disaster" in November).
He may be concerned that Brown won't win the Labour Party nomination or that David Cameron and the Tories are a real threat to win in a general election. The Tories and Liberal Democrats have opposed the war as have a group within Labour. As American-centric as we tend to be, I think this has far more to do with Westminster than Baghdad or Washington DC.