Mr McKinnon, 44, who suffers from a form of autism, is challenging a US bid to extradite him on charges of hacking into highly sensitive military computers eight years ago.

He had been on the verge of being extradited earlier this year after the-then Home Secretary Alan Johnson ruled he should go, despite evidence that he was suicidal.

However, the move was postponed after a judge found that it was “arguable” that extraditing him could violate his human rights.

The Home Office said Mrs May would re-examine the medical evidence for herself to decide whether Mr McKinnon should be extradited.

A spokesman said: “The Home Secretary has considered the proposal from Gary McKinnon’s legal team and has agreed an adjournment should be sought. An application to the court is being made today.”

An adjournment was granted on the case late on Thursday by a judge in the High Court who has asked for an update by the end of July.

Karen Todner, Mr McKinnon’s solicitor, said Mrs May wanted to have “appropriate time” to consider the issues after receiving a request from Mrs Todner.

She said: “I hope this may be a signal of a more compassionate and caring Home Secretary and one that is willing to defend the rights of our citizens.”

Janis Sharp, Gary McKinnon’s mother, said: “We are grateful that the new Home Secretary has agreed to reconsider Gary’s case and we await Mrs May’s decision with great hope that Gary may still have a future.

“Gary is still terrified and undergoing a state of ongoing heightened stress but today’s news gives us hope, at last, that his ordeal may soon be over.

“We need it to be over and totally believe that the new coalition will keep their promises and allow Gary to be tried in his own country.”

Isabella Sankey, a spokesman from campaign group Liberty which has been campaigning for Mr McKinnon, said she welcomed the decision for a “pause for thought” in Mr McKinnon’s extradition battle.

She said: “We hope this might lead to a new approach to extradition that combines international cooperation with justice and compassion.

“This is yet another early test for the coalition parties to honour in government what they promised in opposition.”

Mark Lever, chief executive of the National Autistic Society, said: “Both David Cameron and Nick Clegg have previously spoken out in concern for Gary, and now is their opportunity to take action.

“We heard with relief that Theresa May has agreed to put legal proceedings on hold in order to reconsider Gary’s case once more, and wait in hope that she will be in the position to make the decision Gary and his family so desperately need to hear.”

Last year Mr Johnson had refused to halt McKinnon’s removal, saying he was “of the firm view” that extradition would not be incompatible with his human rights, and “extradition to the United States must proceed forthwith”.

Mr McKinnon was accused in 2002 of using his home computer to hack into 97 American military and Nasa computers, causing damage that the US government claims will cost more than $700,000 dollars (£425,000) to repair.

He admits breaching the systems but denies causing damage and claims he was looking for evidence of UFOs. If he is found guilty he faces spending years

Separately the Government said in its coalition agreement that it would review the workings of the 2003 Extradition treaty. It said: “We will review the operation of the Extradition Act – and the US/UK extradition treaty – to make sure it is even-handed.”

Before the election, the Tories had said they wanted to renegotiate the treaty amid claims it was “one-sided” while the Liberal Democrats – including deputy Prime Minister Nick Clegg – said extraditing Mr McKinnon would be a “travesty of justice”.

A source close to Mr Clegg said today: “Nick has always taken a keen interest in the case but this was a decision by the Home Secretary.”

Critics have long claimed the treaty made it easier for US authorities to extradite Britons to America. Others have complained that it has been used by American authorities to target white collar criminals.

The controversial case has now been considered by six home secretaries.

Source:  http://www.telegraph.co.uk/news/newstopics/politics/7745624/Theresa-May-halts-Gary-McKinnons-legal-battle-against-extradition-to-America.html