The UK and the USA governments were both told by their own experts (as well as by an enormous number of other people oustide the loop) that one predictable consequence of invading Iraq would be to increase the level of terrorism, and to make it easier for the terrorist organisatioins to recruit and to organise.

They decided that in spite of that there were good enough reasons to invade Iraq.

There's no point in trying to rewrite history. They made a decision, knowing there would be a price. And knowing they would not have to pay it themsleves.