Britain followed the US post 9/11 because Bush invoked Article 5 of the NATO treaty, the only time this has ever been invoked.The relationship is nowhere near as special with him in charge. He saw to that.
Iraq and Afghanistan invasions had the majority of Americans (general public, military, politicians) backing it. They were wounded by 9/11 resulting in general support globally too. So I could see why Britain followed. This isnt the case this time. It isnt even getting full backing in America, nowhere near enough support globally, so why should we put our military in the firing line by blindly following this time? If we dip our toe in now, god knows what hellish pit of sh*t, blood and mangled bodies we may eventually end up having to crawl out of. I honestly think that the British public would not stand for it and Starmer writing Trump a blank cheque would have spelt the end for him as PM. Not a fan of Starmer, but he's done the right thing here.
In the past, Britain didn't put our forces in the firing line in Vietnam, no matter how much the US pressed us. This could have been down to us being too broke &/or us having seen our arses over US threatening us to force us to capitulate over Suez, but the ensuing forced devaluation of sterling meant there was no public call for us to back the US so politicians, for possibly the first time in our history, did the sensible thing and kept us out.