The move will see those convicted for consensual same-sex relationships before laws were changed formally pardoned, following a Government pledge to amend the law.

Calls for wider action emerged after Second World War code-breaker Alan Turing was given a posthumous royal pardon in 2013 over a conviction in 1952 for gross indecency with a 19-year-old man.

Turing was chemically castrated and died two years later from cyanide poisoning in an apparent suicide, though there have been suggestions his death was an accident.

Announcing the new plan, Justice Minister Sam Gyimah said the Government would seek to implement the change through an amendment to the Policing and Crime Bill.

Anyone living who has been convicted of the now abolished offences can currently apply through the Home Office to have their names cleared through the disregard process. This removes any mention of an offence from criminal record checks.

Mr Gyimah said: “It is hugely important that we pardon people convicted of historical sexual offences who would be innocent of any crime today.

“Through pardons and the existing disregard process we will meet our manifesto commitment to put right these wrongs.”

However, the Government said it will not support a separate Private Member’s Bill on the subject, which is set to be debated on Friday and proposes a blanket pardon for the living without the need to go through the disregard process.

Mr Gyimah said: “A blanket pardon, without the detailed investigations carried out by the Home Office under the disregard process, could see people guilty of an offence which is still a crime today claiming to be pardoned.

“This would cause an extraordinary and unnecessary amount of distress to victims and for this reason the Government cannot support the Private Member’s Bill. Our way forward will be both faster and fairer.”

Welcoming the Government’s move, Lib Dem leader Tim Farron told Sky News: “The Liberal Democrats continue to be the strongest voice on equality in Parliament.

“This was a manifesto commitment which even in opposition, thanks to the tireless work of our MPs and peers and those from other parties, we have been able to deliver on.”

A Private Member’s Bill by Lib Dem peer Lord Sharkey was instrumental in securing the pardon for Mr Turing.

Lord Sharkey said: “This is a momentous day for thousands of families up and down the UK who have been campaigning on this issue for decades.

“I am very grateful for the Government’s support and the support of many of my colleagues in Parliament.

“It is a wonderful thing that we have been able to build on the pardon granted to Alan Turing during the Coalition by extending it to the thousands of men convicted of sexual offences that existed before homosexuality was decriminalised in 1967 and which would not be crimes today.”

Paul Twocock, director of campaigns, policy and research at charity Stonewall, said: “We welcome the Government announcement to issue a posthumous pardon to all gay and bi men unjustly prosecuted for being who they are, but we don’t think it goes far enough.”

He said his organisation did not agree with the Government’s interpretation of the Private Member’s Bill proposed by MP John Nicolson.

Mr Twocock said: “It explicitly excludes pardoning anyone convicted of offences that would still be illegal today, including non-consensual sex and sex with someone under 16.”

Sky News