The Ting Tong sketch and Walliams blacking up have indeed been removed from iPlayer.
The moral (rather than legal) point is surely whether it is culturally harmful. Something that’s very hard to judge.
Ricky Gervais in his stand-up shows has a sophisticated way of self-exposing all his edgy jokes as containing content he doesn’t agree with in real life and makes the audience feel guilty for laughing at them. Re-working Little Britain to such an extent would be incredibly hard work, but it was acceptable at the time and delighted thousands — people who on the whole did not suddenly become racist on account of it. (The same might be said for the Black & White Minstrel Show adored by many of our parents in their day without feelings of racism).
Educated people on the whole are not racist. They realise it is bad taste to use the n word or even the nk abbreviation when ordering Chinese food. These things mostly become harmful when used routinely and unthinkingly by many of the lower classes.
I say ‘lower classes’ intentionally, not to suggest a person in the upper or middle class is ‘better’ but simply as an observation of cultural difference in a sort of anthropological way. Classes exist, irrespective of whether they ‘should’. One cannot expect a school-drop-out to speak like an Oxbridge man. Won’t happen. But English etiquette evolved (from Victorian times if I’m right) as a means of keeping the lower classes in check and for the upper classes stay in control by what they said and how they acted, without engaging in violence of words or actions (which are the mainstay of much of the lower classes).
These days it is harder to tell. Reese-Mogg, love him or hate him, is upper class. Dan Wootton is lower class but with money. Quite a disgusting state of affairs.