No.
The argument that the UK can’t stand by while it’s allies take action is a strong one, but knee-jerk reactions to horrific events in a quest for vengeance are not a proper reason to go to war. The only justification I’ve heard so far is that we must be seen to be taking action, however ineffective, because otherwise we’ll look like a bunch of cowardly chickens. I don’t know about anyone else, but I grew out of that sort of schoolyard thinking when I was about 12.
Instead of asking if we should take ineffective token action against an ill-defined enemy, they should be asking whether we want to do whatever it takes to solve the problems in the Middle East, and that means 100s of thousands of troops, dead UK servcemen and women, billions of pounds, a probable increase in terrorist attacks here and elsewhere in the west, and sorting out the likes of Israel and Saudi Arabia.