A Briton who hacked into NASA and Pentagon computers has won the right to challenge the government's decision to refuse to block his extradition to the United States, his lawyers said on Wednesday.

Gary McKinnon was arrested in 2002 after U.S. prosecutors charged him with illegally accessing computers, including at the U.S. Defense Department and NASA, and causing $700,000 worth of damage.

The U.S. Army's entire network of more than 2,000 computers in Washington was shut down for 24 hours in what U.S. authorities called the biggest military hack of all time.

Lawyers for McKinnon, who suffers from a form of autism known Asperger's syndrome, say he is not fit to be sent to the United States and that his health would suffer.

But Home Secretary (interior minister) Alan Johnson said in November that the information he had been provided with did not demonstrate that sending McKinnon to the U.S. would breach his human rights, therefore he could not block the extradition.

McKinnon's lawyer Karen Todner said she was delighted with the High Court decision but said the pressure of the proceedings had left her client in a very poor mental state.

I would urge Mr Johnson to review his decision and I appeal to (U.S. President Barack) Obama to withdraw the application for extradition, she said in a statement.

The hearing was expected in April or May, she said, and McKinnon would remain in Britain pending the review.

The Home Office noted the decision and said in a statement that it would not comment further, pending the review's outcome.

A judicial review examines whether a public body came to its decision lawfully -- so Johnson could again allow McKinnon's extradition to go ahead, as long as he followed the right procedures in coming to his decision.

McKinnon has told Reuters he was just a computer nerd who wanted to find out whether aliens really existed. He became obsessed with trawling through large military data networks for any proof that they might be out there.

If convicted by a U.S. court, McKinnon could face up to 70 years in prison.

(Reporting by Kylie MacLellan; Editing by Jon Boyle)