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In It Ain't Half Hot, Mum the wonderful Michael Bates was blacked up as Ragi Ram. I found that bit funny because he was born in India, spoke fluent Hindi and had a love of the country.
Nobody is blacked up in Citizen Khan, it is written and performed by British Muslims, sending themselves up and having the occasional dig at British society.
I think it is very clever how they have they have made their token white person, Dave, the mosque manager, reflecting the token roles ethnic minorities played in British programmes years ago, and indeed Midsomer Murders has been forced to write in to episodes now.