The British forces in Korea were apparently very impressed with the US Marines, and vice versa. I can't remember the source, but a British officer of that era made a comment about the US troops in Korea being a bit soft, and undisciplined. He was asked about the Marines, and replied something to the effect of "No, not at all. I would fight along side the US Marines at any time."
No idea if that's why they are working together now, as they were during the Gulf War. It could just be because the forces complement each other well. British tanks are one of the most heavily armored in the world, but not as fast as ours. Probably more in line with the Marine's tracked APC's which I'm guessing are slower than the Army's. They both fly Harriers, too.
British forces in general seem to have a reputation for going forward slowly, but never going backwards. I wouldn't want to have either group looking for me. They're both nuts - in a good way.