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
A young mother has accused an Uber driver of attacking her after a row over making two drop-offs.
Model Rosie Nelson writes for ITV News, revealing why she is calling for MPs to pass a new law protecting models from becoming too skinny.
Amid calls for new laws to regulate the size of models, we look at how the face of fashion has changed over the past 60 years.