Services at Ealing, CentralMiddlesex, Charing Cross and Hammersmith hospitals are among those that are being affected. Councillor Julian Bell, leader of the council,said:
"We are facing a David versus Goliath struggle to protect our local hospitals but will use every option open to us, including going to court, to fight to keep these vital services for our residents.
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The 20-year-old was found fatally wounded on Roth Walk, near Finsbury Park, north London at around 3am on Saturday, Scotland Yard said.
Police have arrested a man wanted in connection with a burglary at the home of pensioner Richard Osborn-Brooks.
The rally comes after it emerged that the Home Office destroyed thousands of landing cards documenting the arrival of windrush-era migrants