A campaign to pardon nearly 50,000 men convicted under a 19th-century law for homosexual activity is being delayed amid concerns in Whitehall that a small number of paedophiles could be included.

Campaigners who had hoped that the royal pardon for the Enigma codebreaker Alan Turing would be extended across the nation have been dismayed by a warning from Whitehall officials that a blanket pardon could benefit gay men who had sex with a minor.

“There is huge frustration that the deal breaker now appears to be a fear that a general pardon might see what are being described as some paedophiles pardoned,” one source familiar with the Whitehall negotiations told the Guardian. “This sounds like an excuse and is driving people to despair.”

Simon Hughes, the justice minister, will on Saturday pledge that the Liberal Democrats would demand in any future coalition negotiations that a pardon is offered to the estimated 49,000 men convicted of gross indecency before homosexuality was decriminalised in 1967. Hughes will say that the men, of whom 15,000 are believed to be alive, are “morally innocent” of any crime.

Simon Hughes, the justice minister. Photograph: David Jones/PA

The former Lib Dem deputy leader, who will indicate that the Tories have yet to agree to the pardon, will speak up after concerns were raised in Whitehall that paedophiles could benefit from the proposed pardon. Officials have said that there may be no record of whether a minor was involved in a pre-1967 prosecution because homosexuality was illegal regardless of age. Homosexuality was initially decriminalised in 1967 for consenting adults aged 21 and over. The age of consent was eventually equalised in Great Britain in 2001.

Campaigners believe that the objections about benefiting paedophiles could be overcome by introducing two amendments to the relevant legislation to make clear that the men would have acted wholly lawfully under today’s law. The amendments would say that the sex took place between men aged over 16 and that they were both consenting adults.

Turing’s relatives have presented a petition to Downing Street, signed by more than half a million people, calling for a pardon for the estimated 49,000 men prosecuted for homosexual activity. Turing was prosecuted for gross indecency under section 11 of the Criminal Law Amendment Act of 1885, which imposed a maximum prison sentence of two years, after he admitted to having sex with a man. The mathematician, played by Benedict Cumberbatch in the film the Imitation Game, was believed to have taken his own life two years later after avoiding a prison sentence by agreeing to the process known as chemical castration. He was granted a posthumous pardon in 2013 under the Royal Prerogative of Mercy by the Queen after a request from Chris Grayling, the justice secretary.

Hughes will say that the time has come for gay men who did nothing wrong under the law of today to be pardoned. Speaking at a Pride event at Westminster University in central London, the justice minister will say: “There are thousands of men, just like Alan Turing, who have convictions for consenting activity between adults which were only taken to the courts because of the laws of the time which criminalised homosexuality. They are morally innocent of crime and it is time we righted that wrong.”

The justice minister will indicate that the Tories have yet to agree to the pardon. He will say: “If we cannot reach agreement across government before the election, Liberal Democrats will make a commitment in our election manifesto to grant an official pardon to all those convicted in the past of sexual activity which today would be perfectly legal.”

Grayling has supported Hughes as he works with officials in the Ministry of Justice on drawing up plans for a change in the law. Hughes has praised the work of the officials although some campaigners believe that Downing Street is dragging its feet.

Downing Street has pointed out that the coalition changed the law – in the Protection of Freedoms Act 2012 – to allow men convicted of homosexual activity to apply for a “disregard” to make their conviction “spent”. But campaigners say it is wrong that the onus should be on people who committed no offence under today’s law to make an application to the state.