will the uk go to war?

Yes it can happen in Britain considering we've had regular terrorist attacks on British soil for the past 40 odd years it's nothing new.

The British Government didn't even have to balls to sort out British terrorists killing their own here and eventually just let them all go free, so I wouldn't hold my breath that they're going to do much for others

Not sure how you can go to War with terrorists anyways considering they're only suspected terrorists until they actually do something or you have good intel that they are planning to do something. They don't wear uniforms and live in barracks.

The British Army (specifically the SAS) already is deployed in Iraq and Syria fighting ISIS.

yes i know the sas but what about like full blown ie afagnistan