Downing Street has said it has no current plans to alter its policy towards gay men convicted of crimes under draconian gross indecency laws but will “consider” a petition put forward by the codebreaker's family to pardon 49,000 men.

The petition – which has over half a million signatures – states that the “intolerable law brought not only unwarranted shame, but horrific physical and mental damage and lost years of wrongful imprisonment of these men.” The family of Alan Turing, (who according to Winston Churchill “made the single biggest contribution to the allied victory in World War II”) delivered the petition to Downing Street on Monday and demanded that the government pardoned the other 49,000 gay men estimated to have been persecuted, like Turing, for their homosexuality.

Turing's mathematical skills were critical in cracking the Enigma military codes during the allied war effort against Nazi Germany. But in 1952 he was convicted of gross indecency with a 19-year-old man and, as a result, chemically castrated. He died two years later from cyanide poisoning.

The offence that Turing was prosecuted for - Section 11 of the Criminal Law Amendment Act 1885 - stated:

Any male person who, in public or private, commits, or is a party to the commission of, or procures, or attempts to procure the commission by any male person of, any act of gross indecency with an other male person, shall be guilty of a misdemeanour, and being convicted thereof, shall be liable at the discretion of the Court to be imprisoned for any term not exceeding two years, with or without hard labour.

A spokesperson for No 10 tells the New Statesman:

This government has already taken action to allow those convicted under these types of laws to apply for a disregard – this means that their conviction is treated as spent, meaning it doesn’t turn up in any criminal records checks. Since the commencement of the Protection of Freedoms Act 2012 those living with convictions under laws against homosexuality have had the option of applying to the Home Office for a disregard. In terms of the petition itself we are aware of it and aware of the support for pardoning those who were convicted under these laws. In terms of what they want, in terms of pardoning those who are convicted – there are some real practical and legal complexities, with the position we have already taken and actually issuing pardons. But what I can say is that we are looking carefully at what more we can do to right these wrongs. In the case of Alan Turing – that was an exceptional case – but there are no current plans to change policy. But we will of course consider the petition, as we do with all petitions.

Matthew Todd, the editor of Attitude magazine, who visited Downing Street alongside Turing's relatives, tells the New Statesman that the 500,000 people who signed the petition will not think this response is good enough. Todd adds: "Lives were ruined because of these laws. Families were ripped apart by the convictions and the shame that their loved ones were subjected to. David Cameron's championing of equal marriage is to be welcomed but it does not hide the fact that a majority of his MPs did not support equal marriage. The Conservative party still has a lot to do to convince LGBT voters that it regards us as worthy of the same respect as the rest of the population."

As David Allen Green - the New Statesman's former legal correspondent - argued in a blog in 2013, the Protection of Freedoms Act 2012 (the government's current policy) is only for those still alive. Turing's conviction was one of thousands and there is no logical reason why his should be regarded as a unique case. Allen Green wrote: "If Alan Turing is to be pardoned [he received a posthumous royal pardon in late 2013] then so should all men convicted under section 11 if the facts of their cases would not be a crime today." He continued: "But a better posthumous gesture would be to simply extend the 2012 scheme to all those who are now dead. Removing the criminal records completely of all those prosecuted who would not be prosecuted today on the same facts would be a better legislative gesture than a single statutory pardon, if there is to be a legislative gesture at all."

Rachel Barnes, Turing's great-niece, was among a gathering of the codebreaker's relatives on Monday. She said: “I consider it to be fair and just that everybody who was convicted under the gross indecency law is given a pardon. It is illogical that my great uncle has been the only one to be pardoned when so many were convicted of the same crime. I feel sure that Alan Turing would have also wanted justice for everybody.”

Barnes has hit the nail on the head. It is illogical. Yes, Turing led a team decoding messages from Nazi Germany at Bletchley Park. Yes, his work helped shorten the brutal conflict and save thousands of lives. But, his "crimes" - for which he received a posthumous royal pardon - are no different from what the thousands of other gay men received vindictive convictions for. They too, should be pardoned. It would be a gesture to the families of those gay men who have passed away and cannot apply under the 2012 Act to have their criminal records wiped. A pardon will act as an apology for previous British governments who have wrongfully punished their citizens on the basis of their sexuality. Irrespective of "practical and legal complexities", a broad-sweeping pardon would "right these wrongs". It would also fit in neatly with the Tories' "long-term economic plan": it would cost the state nothing.

Update (03/03/2015) -In an interview with Gay Times magazine the Labour leader, Ed Miliband, has pledged that a future Labour Government will offer posthumous pardons for gay men convicted under the historic indecency laws. The new legislation will allow relatives of the deceased men to apply to the Home Office to quash convictions under the gross indecency laws for consensual same-sex relationships. Miliband said to GT: “I think it’s a stain on our society, frankly. I think it’s right what’s been done in relation to Alan Turing and his family, but there are also other families that will have had relatives who were convicted, as I say, simply because of the person they love. And I think it’s time we acted for them, too. I think we owe it to the LGBT community to make this move.

“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.”