I, unabashed reviler of Blair as I may be, believe that 9/11 gave this reprobate a new lease on political life. Whereas even the Brits were about ready to give this ferret his walking papers, because of the problems you reference, he was actually able to capitalize on the WOT.
He joined himself to GWB's hip in an about-face. Previous to the Twin Towers, he was a very vocal opponent of the man. He merely remained a left-wing lapdog of Bill's while using GWB and the War on Terror as patriotic cover.