Mr Keates said Princess Eugenie should revoke her patronage of the Print Room in recognition of the controversy surrounding the play.

He told the Daily Mail: “As a representative of British East Asians in this country, I do not see how she could lend her name to a theatre that is not supporting racial equality, either actively or through ignorance.”

Supporters of the Princess defended her patronage of the Print Room, saying her role had nothing to do with the details of particular productions staged there.

Equity, the trades union representing actors and performers, has backed the protests over the casting of In the Depths of Dead Love.

Christine Payne, Equity general secretary, says: “This casting clearly shows that the Print Room is not engaging with the industry-wide discussion on diversity.”

But the Print Room defended its choice of casting, pointing out that In the Depths of Dead Love is not a Chinese play and that the characters are not Chinese.

In a statement it said: “The production references a setting in Ancient China and the characters’ names are Chinese. These are literary allusions in Howard Barker’s fable and never intended to be taken literally.

“It is, in fact a very “English” play and is derived from thoroughly English mores and simply references the mythic and the ancient. It has therefore been cast accordingly.”