A strongly-worded letter from US attorney general Eric Holder was due to be delivered to Mrs May's office at the Home Office last night.

The row over Mr McKinnon has turned into the biggest cooling in trans-Atlantic relations since Lockerbie bomber was released three years ago.

Senior US officials are now understood to describe the relationship between the Obama administration and Mrs May as "finished".

Mr Holder is understood to feel "completely screwed" by Mrs May's decision not to extradite Mr McKinnon because of doctors' fears that he might kill himself, complaining that the US has wasted million so pounds on legal fees for the case.

The Daily Telegraph understands that Mr Holder has refused to return Mrs May's phone calls since her surprise announcement on Tuesday.

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The depth of ill-feeling could jeopardise co-operation with the US over security because Mrs May leads for the UK in talks with Washington.

A senior administration official said: "This was a cheap political trick by Theresa May to further her political career.

"Mrs May told us in July that there were no legal or medical grounds to block his extradition, and then she changed her mind without having the decency to inform us."

The official said the row had comparisons with row over the Scottish Government's decision to release Lockerbie bomber Abdelbasset Al Megrahi in 2009.

The source said: "After all the controversy over the release of the Lockerbie bomber to Libya on humanitarian grounds, this decision on Gary McKinnon does not inspire confidence that the British government is serious about dealing with serious security issues."

As late as Monday evening, American officials were so sure that Mrs May would extradite Mr McKinnon that they had prepared a plane to come to get him.

Mrs May has a quasi-judicial role as home secretary to decide on extradition cases. Her last minute decision to block Mr McKinnon's extradition surprised many of Mr McKinnon's supporters who had been expecting bad news.

Mrs May made her decision on Tuesday morning, informing Prime Minister David Cameron and his deputy Nick Clegg just before the Cabinet met.

American officials learned of Mrs May's decision when she told MPs that she would block Mr McKinnon's extradition on human rights grounds.

Mrs May told MPs on Tuesday that the decision to block Mr McKinnon's extradition was "exceptional", which could suggest she was trying to stop lawyers using her ruling as a precedent to frustrate the extradition of alleged terrorists

But the US is now concerned that other defence lawyers will use the fear that terror suspects might kill themselves to block future extraditions.

The source added: "This decision means that every single person who faces to the extradition to the US can have it blocked on the basis that they might commit suicide."

American officials were surprised by the sudden change in stance because Mrs May told Mr Holder in a letter on July 12 there were no legal or medical grounds to block McKinnon's extradition to the US.

According to former Labour home secretary Alan Johnson, Mrs May admitted to Mr Holder in July there were also "ramifications for national security" if the extradition was blocked.

A Home Office spokesman said: "We do not routinely comment on Ministerial correspondence."