A cross-party group of MPs will demand the government amend the UK-US extradition treaty this evening, amid fears it is unfair on British citizens.

Of particular concern is the case of alleged computer hacker Gary McKinnon who has been fighting extradition on health grounds for six years.

McKinnon, who is accused of hacking into the Pentagon in order to search for evidence of UFOs, suffers from Asperger’s syndrome and his supporters argue he should serve any sentence at home in Britain.

Among the MPs who have signed the motion are former Conservative shadow home secretary David Davis, Labour chair of the Commons home affairs committee Keith Vaz and former Lib Dem leader Menzies Campbell.

The MPs who pushed for the debate are hoping a victory for their side would put pressure on ministers to renegotiate the treaty.

Tory MP Dominic Raab, one of the leading figures pushing for change, said the process needed to be more transparent and should be in line with the treaties the US has with countries such as Australia.

"The data shows that five Americans have been extradited to the UK under the new regime, 29 British citizens the other way. I think the key issue here, no-one is suggesting abolishing extradition, but it's about reform," he told the BBC's Today programme this morning.

"The key issue in the American treaty is 'forum'," he said. "So where you have cross-border cases like Gary McKinnon, where should it be decided and who decides? At the moment it's done by sort of haggling between prosecutors behind closed doors.

"Actually it should be done openly in court. And just by the way, the US has treaties with Mexico, Brazil and Australia, giving their authorities much greater discretion to refuse to extradite their citizens.

"So why shouldn't Britain, a stalwart ally, ask for this very modest change? And I think it's important that both countries depoliticise this and I think a forum clause would help us achieve that."

But former Labour home secretary David Blunkett said Raab and other MPs concerns were "based on a myth".

"It's based on the fact they believe there is a substantial difference between what we agree in terms of our own citizens and what the Americans agree for theirs - there isn't."

And a recent review into the treaty conducted by the former Court of Appeal judge Sir Scott Baker concluded the treaty "does not operate in an unbalanced manner”.

However, the parliamentary Joint Committee on Human Rights recently said that "safeguards" to protect British citizens needed to be brought in.

The text of the motion to be debated this evening in the Commons calls for the government "to reform the UK’s extradition arrangements to strengthen the protection of British citizens by introducing as a matter of urgency a Bill to enact the safeguards recommended by the Joint Committee on Human Rights".

The American ambassador to London, Louis Susman, has insisted that the treaty is fair and that criticisms that it is unbalanced are based on a misunderstanding of its function.

Writing in the Daily Telegraph on Monday, he said the US-UK treaty in its current form was "fair and balanced" and “didn’t need to be changed”.

"In an age of international crime syndicates, global terror networks and cyber attacks, my government strongly supports the US-UK Extradition Treaty as an essential tool for bringing criminals to justice," he said.

He added: "It is worth noting that the United States has never denied an extradition request from the UK under the present treaty."

Officially Downing Street has not ordered coalition MPs to vote a certain way, but it has been reported that they are putting pressure on backbenchers behind the scenes to vote against the motion.

MPs are also concerned about Britain's extradition arrangements with the European Union and the operation of the European Arrest Warrant.