Gay men with convictions for homosexual activity under historical indecency laws will be pardoned under a Labour government, Ed Milband pledged yesterday.

New legislation known as Turing’s Law — in memory of Enigma codebreaker Alan Turing, who was given a posthumous pardon in 2013 for a 61-year-old conviction — will allow family and friends of men who have died to bid for their names to be cleared.

It will apply to convictions under old gross indecency laws against men who had consensual same-sex relationships.

The Labour leader said: “What was right for Alan Turing’s family should be right for other families as well.

“The next Labour government will extend the right individuals already have to overturn convictions that society now see as grossly unfair to the relatives of those convicted who have passed away.”

Dr Turing was chemically castrated following his conviction for gross indecency in 1952 and died of cyanide poisoning two years later aged 41.

He was granted a pardon under the Royal Prerogative of Mercy by the Queen.

Campaigners, including the codebreaker’s family and actor Benedict Cumberbatch, who played him in The Imitation Game, have called for the pardons to be extended to tens of thousands of other British men convicted under old laws.

Turing’s great-niece Rachel Barnes (pictured) said: “I am delighted to hear that a new Labour government would bring in a new Turing law to grant pardons to all gay men who were convicted under the gross indecency act.

“This will bring justice and peace to the men and their families who were convicted.”

A petition on Change.org calling for pardons to be granted to men convicted for consensual relationships under the law has been backed by more than half a million people.