Isn't that the kind of logic which whipped someone into such a frenzy that they murdered a Labour MP last year?

The cnut who did the Manchester attack was born in this country in 1994, 3 years before Labour regained power. The cnut who did the Westminster attack was born in this country over 50 years ago. To pin the global rise of Islamic extremism purely on previous Labour governments' immigration policies doesn't make sense, whether you agreed with the policies or not.
I'd say the biggest impact Blair et al had on creating the current climate is unnecessarily getting us involved in a war we didn't need to get involved in.