Relevant to OP's question, I've heard stories of incidents in which white American servicemen would attempt to enforce segregation (or otherwise attempt to make life unpleasant for their black colleagues) in pubs shared by both US and British forces, and the British personnel would not take too kindly to the concept - often coming to blows over it.
Is there any truth in that?
EDIT: I left a "that" lying around.
George Orwell, an editorialist in England during war time, addresses that question. He raises two important arguments:
Lack of credit for the English war effort. He feels that both the British government, with its policy of not criticising USA, and the American press, which glorifies everything American, are taking credit for much of the Allied success.
Difference in pay between the two armies. The American soldier was paid five times more than his British counterpart (according to Orwell, I read it was 3 times from other sources), including a more generous daily ration of cigarettes and coffee.
Orwell remarks how the British soldiers are resentful due to the two points. In addition, they cannot fraternize together during training or the time they are stationed in England since the difference in pay leads to different lifestyles and hobbies.
Source: http://www.telelib.com/authors/O/OrwellGeorge/essay/tribune/AsIPlease19431217.html
While I can't offer a comprehensive answer, I do have something to contribute.
To entertain their soldiers, the allies provided their troops with comics. While the comics gave their soldiers a distraction from the terrible war they were fighting, you can only read a comic so many times before it gets tired. The British soldiers were given Jane Comics, a branch of romance comics that more or less became pornography, while the Americans were given Superman.
When the Americans came to Europe, they met with the Brits and traded comics. This wartime comic trading is attributed to the proliferation and popularization of Superman in Europe, considering Superman had so recently come out at the time in 1939.