I see what you're saying, but right now, like the American army, the Brits are spread thin. Neither the US or the UK want to be in a position, which we are already, where we'll endanger more of our men.
If the Brits attack, I know the US, without question, will back them up 100%. Speaking of the Falklands War, which I was old enough to live through and watch on a daily basis, the US gave the Brits "information" on the A-4, which helped the Brits out. Not that they needed help shooting down the A-4 but being the closest allies, the US shared this info w/them.