The former international development secretary, Andrew Mitchell, has joined forces with radio presenter Paul Gambaccini and comedian Jimmy Tarbuck to press for greater protection for people under investigation over historical sex abuse allegations.

Mitchell has personally lobbied the justice secretary, Michael Gove, over the issue and said that Gove – who also holds the title of lord chancellor – was giving “serious consideration” to the mounting concerns about the way in which high-profile figures have been wrongly accused of paedophile acts.

“I think the treatment of Paul Gambaccini by the British justice system was a disgrace,” said Mitchell, who accompanied the veteran DJ to a meeting with Gove shortly before Christmas, when Tarbuck’s concerns were also aired. Both Gambaccini and Tarbuck were arrested and questioned by police investigating historical child abuse allegations, only to be told months later that no case would be brought against them.

After his arrest, Gambaccini described the allegations as “total fiction” and added: “I knew the so-called file on me wouldn’t have anything in it.” Appearing before a House of Commons select committee in 2015 to give evidence, he said he believed he had been used as a human “flypaper” to encourage other people to bring similar allegations against him, adding that he had lost more than £200,000 in earnings and legal costs.

Tarbuck was arrested by North Yorkshire police over claims that he had assaulted a boy in Harrogate during the 1970s. After his arrest he was later investigated over six separate allegations. After the case against him was dropped on the grounds of insufficient evidence, Tarbuck expressed his distress at the accusations. “The real thing that annoys me is these people can remain anonymous,” he said, adding that the experience had shown him “who your friends are, your real mates”.

The two are among a number of high-profile figures, both living and now dead, who have been accused of sex abuse. Allegations against Edward Heath, the former Tory prime minister, have been rejected by his friends. “We had a new low for the British justice system when a police officer stood outside the house of a most distinguished former prime minister and effectively labelled him as a paedophile,” Mitchell said.

There is growing disquiet about the way Sir Cliff Richard has been investigated, with police tipping off reporters before the singer’s home was raided. “It’s hard to comment on Cliff Richard because at the moment there are, I believe, ongoing state inquiries,” Mitchell said. “But on the face of it it’s already clear he has been treated in a most inappropriate way.” Richard has denied the allegations of abuse.

Mitchell, who was at the centre of the Plebgate affair – a row that hinged on what he had said to police on duty at Downing Street – said calls for changes in the law were being heard by the Ministry of Justice. “There is huge and widespread concern on all of these counts, and we went to see the lord chancellor to express those concerns. The lord chancellor listened. Clearly, there is forthcoming legislation and the lord chancellor undertook to give serious consideration in framing that legislation to what we had said to him.”

Concerns about the way police investigate historical sex abuse allegations resurfaced last week when the former head of the army, Lord Bramall, 92, was told by the Metropolitan police that he faced no further action after it had investigated claims against him. Bramall, a D-Day veteran, was never arrested and denied the allegations. His son, Nicholas, said the man who accused his father, known as “Nick”, had been “peddling unsubstantiated and uncorroborated information” and called for him to be investigated.

“The treatment of Lord Bramall adds a new tier to all of this that should shame every one of us,” Mitchell said.