Many find Tony Blair distasteful....but he is a brilliant debater and strategist (compared to the colorless Gordon Brown and David Cameron), plus a man has to eat.
On the Iraq invasion, my own armchair shot-in-the dark analysis is that the Americans did not give UK a choice. I think they threatened to cut off the UK from intelligence/military support in terms of financing, access to assets, information and the formidable product of institutions like the NSA...the UK would have been very vulnerable and badly exposed; rightly or wrongly, the leadership's inner sanctum must have felt like a deer caught in the headlights, and so Blair used his considerable powers of persuasion and dragged all of UK into war.
And back to the present. There is no room for emotions in diplomacy and international politics. It is unavoidable that states have to deal with other states they are uncomfortable with, and men like Blair step in to bridge gaps like these. Guys like him are necessary. An unpalatable fact, but fact all the same.