Blackface was not originally using makeup to change your skin colour, it was the disgusting
parody of black people - in the UK infamously illustrated by the "The Black and White Minstrel Show
WP".
I would argue that the "blackface" in Little Britain is "acceptable" as they are creating and acting as different characters and when playing a non-white character being black/non-white was just one of the character's attributes, not the focus of the character. The two creative people behind Little Britain are white males, I would say it would have been more wrong for them not to include characters that are "representative" of Britain today. They dress up as a variety of non-white male characters. From my memory there is one character that I think was probably not OK and that was the "mail order bride" that I think was meant to be from Thailand. For that character being "asian" was the focus of the character.
(All this is from memory so I may not be remembering the extent of their use of non-white characters so what I've said above may be completely wrong!)