The Home Office, however, appears to be standing firm, claiming that there is no imbalance in the UK-US extradition treaty and no need for a review.
As reported previously by Infosecurity, the 43-year-old UFO hacker McKinnon is alleged to have gained unauthorised access to the Pentagon's military networks in a bid to discover evidence of the existence of alien life and UFOs.
McKinnon's lawyers have argued many times that extraditing their client would lead to "disastrous consequences" for the health of the UFO hacker, including possible psychosis and suicide.
It now transpires that a House of Commons committee is conducting an inquiry into the US-UK extradition treaty, which critics say does not treat American and British citizens equally.
In a just-published letter from committee chairman Keith Vaz to Alan Johnson, the Home Secretary, Vaz said the MPs had received "clear, legal opinion" from two lawyers that the home secretary had greater scope to exercise his discretion in UFO hacker McKinnon's case than the minister believed.
The letter urged the Home Secretary to comprehensively review the operation of US-UK extraditions and exercise discretion in the case of Gary McKinnon.
The letter adds that there is a serious lack of equality in the way the extradition treaty deals with UK citizens compared with that of US citizens.
In a carefully worded statement, however, the Home Office said there is no imbalance in the extradition arrangements between the UK and the US.
"As the Home Secretary told the Home Affairs Select Committee on Tuesday, the evidence that must be provided for a US extradition request to proceed in the UK is in practice the same as for a UK request to proceed in the US", said the statement.
"The suggestion that the operation of the Extradition Act needs to be reviewed comprehensively is unnecessary", it added.
A slight glimmer of hope is in the statement in that it says that the Home Secretary is looking at new medical evidence on McKinnon, which Alan Johnson has said he will consider very carefully before approving extradition.
Infosecurity notes that this is a curious comment to make, as it was the previous Home Secretary, Jacqui Smith, who formally approved the UFO hacker's extradition.
Johnson's statement adds that he intends to give McKinnon's lawyers time to examine medical reports and make legal representations to the European Court of Human Rights in Strasbourg.
"Unless the evidence shows that extradition would breach the European Convention on Human Rights it would be unlawful to refuse extradition", said the statement.