Generally foreign policy (at least as far as relations between allies, as opposed to troops-out-of-Whereverstan) does not play a big part in elections on either side of the Pond. I'm not suggesting an election going differently in the US is automatically going to flip a subsequent one in the UK, much less the other way around--not unless the election is so close that a tiny difference could flip it. But this thread is for discussing consequences from different elections on one side of the Pond that could nonetheless have a certain effect on the other, if not so dramatic.
For example, take 1992. If the Conservatives had lost in the UK and Kinnock had announced a less pro-American foreign policy...well in the US Bush was going to lose a few months later no matter what happened, but something like this could be disproportionately important, just because Bush staked so much on his foreign policy record and the Gulf War, and his opponents could spin Kinnock's moves as "this Gulf War you say went so swimmingly, well the voters in our closest ally seem to disagree". It wouldn't change the overall result, but it might make Bush's defeat even worse.
What other examples of this type can you think of?