Adam Tidman, 34, died in hospital on February 11, over two weeks after officers restrained him in Borough High Street on January 25.
Police were called to around 12.55am to reports of a man causing a disturbance.
They found security staff at Belushi’s restaurant restraining Mr Tidman, and officers continued to restrain him outside the entrance.
While being restrained, Mr Tidman became unwell and was taken to hospital by paramedics.
At the time, the Metropolitan Police said he was in a “life-threatening” condition, and 17 days later he died.
The incident has been referred to the Independent Office for Police Conduct (IOPC) to investigate the matter.
An appeal has been launched for any other witnesses to come forward.
IOPC director Amanda Rowe, said: “We would like to pass on our thoughts to Mr Tidman’s family and all of those affected by this incident.
“It’s possible that a number of bystanders may have witnessed him being restrained on Borough High Street or the events that led up to it.
“It’s vitally important that we establish the full circumstances leading up to the man’s death and therefore we’re appealing to anyone who saw what happened to contact our investigators to help us to establish all of the circumstances surrounding his death.”
An inquest will be opened in due course, the IOPC said.
Any witnesses are asked to email BoroughHighStreet@policeconduct.gov.uk or call 0300 303 5592.
