Consultants and MPs opposed to plans to close Lewisham's Accident and Emergency department have handed letters and a 20,000-signature petition to Downing Street.
Protesters, including Lewisham East MP Heidi Alexander, say the closure would leave them with one accident department for 750,000 residents.
The planned closure is part of a reorganisation aimed at saving the South London Healthcare Trust after it went into administration.
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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.