The left wing liberals love to crow that it was, but really it was irrelevant for most people, and had absolutely no impact on Blair leaving or Labours fall. They even won an election after the fall of Iraq.

Blair left, he wasn't pushed, he knew they'd spent far more money than the UK could afford, had run up huge bills on the welfare state, NHS, public service workers. Brown had always wanted power, the deal had always been to give it to him, so after 10 years in power and facing the end, when the defining New Labour policies were Spin and Overspending (with a lot of one to hide the other), he walked. The crash happened a year later and Brown, who never had any charisma, and New Labour, were done.

I never liked Tony Blair, I never liked his policies on most things, I despised New Labour... but if he had stuck around, and gone for the 2010 General Election, I'm not sure he wouldn't have won.