Rosa Curling, a lawyer with solicitors' firm Leigh Day who is acting for the campaigners, said:
"This is a tremendous victory for all the people of Lewisham and for the thousands who have campaigned for this well-run, successful hospital to remain open.
"This mobilisation of the public in support of Lewisham Hospital has been extraordinary. Motivated by injustice, those who have campaigned for its survival have successfully shown that the decision taken by Jeremy Hunt to downgrade and close many of the hospital's services was wrong and unlawful.
"Real questions must now be asked about the decisions being taken by this Government in relation to healthcare.
Jeremy Hunt cut services at Lewisham Hospital because of financial difficulties faced by its neighbouring trust, South London Healthcare.
"These difficulties were caused by disastrous PFI contracts entered into by South London, which were costing #60 million a year to service.
The court found Jeremy Hunt had acted outside his powers by trying to make Lewisham pay for the financial problems of its neighbour.
"The Secretary of State cannot respond to the financial difficulties caused by the Department of Health's damaging PFI policy by simply imposing cuts on NHS services from above.
"This judgment should serve as a warning to the Government that, if they try to do this, local communities will fight back to ensure their healthcare services remain in place."
More top news
Public services union Unison says it will nominate Jeremy Corbyn in the Labour Party leadership contest.
Google search now shows you when businesses and attractions are busiest.
The planning application said the museum would be dedicated to celebrating the achievements of East End women. Residents are very angry.