Actually, they did - but it wasn't anything glaringly obvious. Tony Blair upset quite a lot of people when he decided to go to war - he had already been trying to steer his prime ministerial role closer to a presidential one and saw his position as "Commander-in-chief" a very important one. Iraq saw a massive protest in Britain which, although didn't damage the Labour party, damaged Blair's reputation as a whole; not the least with his cabinet, who, although were all allies to blair and held collective cabinet responsibility, felt Blair had made a bad mistake and soon raised a stink about it.
In the long term, Blair would have the Iraq war on his head, it would be a label that many British people would stamp on him. Blair had promised to give British people more direct democracy, which he had done so with the Good Friday Agreement in 1998, Human Right's act (Supposedly) and devolution in Scotland and Wales. He had failed to achieve any electoral reform and was criticised for his reforms on the House of Lords, which some say didn't go far enough. After the invasion of Iraq, there was a definate change in the wind in opinion towards Blair and even though he was never voted out, he was soon voted as one of Britain's worst Prime Ministers - as according to several polls.
Although we may never see Tony Blair found a war-criminal, it was certainly damaging to him to have been put on an inquest. It is ironic that he is now peace ambassador for the middle east - but nevertheless, Tony Blair is one of the leading prime ministers in history - in that he is well known and either loved or hated - but the Iraq war is a universally controversal objective which will loom over the history of Blair's premiership indefinitly.