Benedict Cumberbatch has urged Prince William and Kate to act on a campaign to pardon tens of thousands of gay men convicted alongside Imitation Game codebreaker Alan Turing.
Stephen Fry and gay rights campaigner Peter Tatchell have also added their names to the open letter calling for action.
Cumberbatch, nominated for an Oscar for his role as Turing - a pioneering computer scientist who helped crack the Enigma code, wants a pardon for 49,000 other men prosecuted because of their sexuality.
Turing was convicted of gross indecency in 1952 for being gay, and committed suicide two years later.
In a letter to the Government and published in The Guardian, campaigners are calling for the royal family to act and convince the Government to pardon all those convicted under the outdated law.
It states: "The UK's homophobic laws made the lives of generations of gay and bisexual men intolerable.
"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 a pardoning all the men, alive or deceased, who like Alan Turing, were convicted."
The letter is also signed by Morten Tyldum, director of The Imitation Game, Rachel Barnes, Alan Turing's niece, and Matthew Todd, editor of Attitude Magazine.
They write: "Alan Turing was one of the greatest heroes of the 20th century, a man whose work on the machines that deciphered the Enigma codes helped win World War II and who was pivotal in the development of modern computers.
"Winston Churchill said Alan Turing 'made the single biggest contribution to the Allied victory in World War II'."
But in 1952, just a few years after peace was declared following the Second World War, Turing was prosecuted and convicted of gross indecency under Section 11 of the Criminal Law Amendment Act 1885.
In 2009, an "unequivocal apology" for his appalling treatment was issued by then prime minister Gordon Brown.
The Queen granted the scientist a posthumous pardon under the Royal Prerogative of Mercy in 2013.
But the campaigners say this should be extended to all men who fell foul of the law.
It states: "The apology and pardon of Alan Turing are to be welcomed but ignores over 49,000 men who were convicted under the same law, many of whom took their own lives.
"An estimated 15,000 men are believed to still be alive."
Their petition has been signed by 40,544 people.
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