Maybe it was because they knew that a squad of well trained clams could have done as much damage as Black Buck did and didn’t want to be associated with it?
As to RAF Diego Garcia, it would seem the UK has a vested interest in it existing. Rumour has it a Vulcan even landed there once or twice.
Lacking any Vulcans, maybe letting the US assume the missions, foot the bills, and take the bad press is a good idea.