Actor Benedict Cumberbatch is among some 75,000 people to sign a petition urging a pardon for all gay men convicted of indecency in Britain under historic laws.

Cumberbatch is Oscar-nominated for his role as gay mathematician Alan Turing, whose code-cracking skills helped Britain fight Germany in World War II, in the film The Imitation Game.

Turing was convicted of gross indecency in 1952 and underwent chemical castration before committing suicide two years later.

Homosexuality was decriminalised in England in 1967 and Turing was given a royal pardon in 2013.

An open letter published in the Guardian newspaper on Saturday urged Prince William and his wife Catherine to step in to make the case for a blanket pardon for the 49,000 men who were convicted.

However, a spokesman for the royal couple said that it was a government issue and they would not be making any public comment.

"The UK's homophobic laws made the lives of generations of gay and bisexual men intolerable," the letter said.

"It is up to young leaders of today including the Duke and Duchess of Cambridge to acknowledge this mark on our history and not allow it to stand.

"We call upon Her Majesty's government to begin a discussion about the possibility of pardoning all the men, alive or deceased, who like Alan Turing were convicted."

Other famous signatories included British actor and comedian Stephen Fry and the director of The Imitation Game, Morten Tyldum.