You don't seem to get it Eversor. Any time one of our allies backs out because they were attacked, that strengthens the terrorists who are seeing their tactics work. And if their tactics work then they will continue them even longer and cause even more bloodshed. If Britain, being the largest ally we have, pulled out because of this then it would be a huge blow to Coalition morale and a huge boost to the terrorist morale, emboldening them to do even more drastic measures.
Now, Britain is far more than just a "political ally". They have 12,400 troops total in the Middle Eastern theatre, which is nothing to sneeze at. And, the other 24 allies that actually have troops on the ground surpass that number, proving that a little can make a lot.
No, no, no. You don't support it. The majority do support it or at least tolerate it. Otherwise the Labour party, and Blair, would have been ousted from government in the last election, but they weren't. The anti-war people in America, Australia, and Britain may be louder than the pro-war, but that by no means makes them the majority. The recent elections of all three of those countries prove there is a "silent majority" that approve or tolerate what is going on.
Democracy: rule by the stupid