Iranian authorities had proposed Richard Jan – a biochemist described as the country’s “worst stalker” – in exchange for the Foremans’ in conversations with the Government and the Foreman’s family.

A Government spokesman, however, has robustly denied the claims.

He told the Telegraph there was “no truth whatsoever to the claims of a potential exchange arrangement, and giving credence to these claims is not only wrong, but risks hindering all the other efforts currently being made by this Government to secure the Foremans’ release”.

Justice Secretary David Lammy also told Sky News that while prisoner swaps can be made, “the specifics on this would not be right”.

“And I’m not sure from what I’ve heard that this is… credible,” Mr Lammy added.

In January last year, Iranian authorities sentenced the couple to 10 years in jail for espionage after the Government claimed the pair had “gathered information in multiple provinces of the country” as they travelled through the country on a round-the-world motorcycle journey.

Lindsay and Craig Foreman were arrested in Iran after being accused of espionage during a motorcycle tour

The Foremans were not allowed to attend their own appeal hearing, which they lost in Iranian courts on Tuesday.

In 2004, Jan was sentenced to life after being found guilty of stalking and attacking 200 people.

Over 1,000 statement were taken by prosecution against him, and 109 witnesses – mostly working in health care and local government – testified against him.

Richard Ratcliffe, whose wife Nazanin Zaghari-Ratcliffe was previously detained in Iran, has said cases such as the Foremans were used to send political signals, adding that the family was “caught in a fight between two governments”.

David Lammy claimed the ‘specifics’ of the prisoner exchange ‘would not be right’ | GETTY

The Government has strenuously denied claims it pushed back against talks of a prisoner exchange

Mr Foreman, speaking from Evin prison in March, urged Sir Keir Starmer to help him and his wife, warning of worsening conditions.

Admitting that he was “genuinely scared”, Ms Foreman’s son, Joe Bennett, previously told GB News: “We are now genuinely worried for their lives because of what’s going on, and the implications of the actions that are being taken by the US and Israel.

“I think they’re bearing up, but it’s a tough gig for them mentally, physically, and spiritually because the system is made to break people, that is what it is intended to do.”

After the remarks from Mr Lammy, he told Sky News he hoped the Government would “shift” in the approach to his mother and stepfather’s case.

He said: “The question that we wanted to ask as a family is, if this isn’t the solution or a proposed solution, then why not?

“Anything can be done in theory, but it’s been a long time coming where it gets the attention it warrants.

Joe Bennett, son of Lindsay Foreman, said he hoped the Government would ‘shift’ its approach to his mother and stepfather’s case

“And the conversation to be had, at least we can either get a proposed path to their release or closure that this isn’t a solution.”

Yvette Cooper, the Foreign Secretary, said the pair’s arrest was “unjustifiable” and said the Government was continuing to press Tehran “relentlessly” for the couple’s release.

Sir Jeremy Hunt – who served as Foreign Secretary while Ms Zaghari-Ratcliffe was imprisoned in Iran – told the Government to – with caution -do “everything it possibly can” to free the Foremans.

He said: “Obviously, what you don’t want to do is something that leads to the next person being illegally detained by the Iranians.

“So you have to be careful that you don’t reward the kind of absolutely despicable behaviour that we’re seeing from Iran, one of the very few governments in the world that will arbitrarily detain an innocent person as a tool of diplomatic leverage.”