Police are appealing for witnesses to an incident in Vauxhall at approx 8.30pm on Sunday 30 October.
A man was found suffering head injuries at the bottom of steps leading to the Vauxhall Cross footbridge, close to Albert Embankment.
The man – believed to be in his 60s – was taken by London Ambulance Service to a South London hospital. His condition is described as critical.
Police believe that they know the identity of the man, but are yet to contact next of kin.
CID officers based at Kennington are investigating. Anyone with information that may assist police should call CID on 020 8649 2474.
Police are particularly keen to hear for an American man – believed to have medical expertise – who spoke with ambulance staff at the scene.