From what I understand the British weren't willing to get into fights over it. They just told any non-white officer (and in WW2 there wouldn't have been too many of them) or NCO that they would not be welcome in a US mess. And to try and be sensitve to US officers who might have a problem with a non-white officer in a British mess, but not throw the non-white out. Ignore the racism for the good of the alliance basically.
Not really, When General Hawes was expectimng his first batch of Black troops to his command in britain he asked for Britain to enforce segregation, they told him to get stuffed.
Sir James Grigg did support segregation but he too was told to get stuffed.
The British home office issued a decree that any attempts to enforce segragation by the US authorities in Britain would result in a withdrawel of co-operation.
It didn't stop some politicians like the conservative Maurice Petherick suggesting that all Black troops should be sent to Italy to fertilise the Italians as the Italians were used to it anyhow, but hey he was just a small town Tory and they never really change do they.