Officers were called to the scene at around 12.40am on Saturday, June 3, to reports of a man collapsed after being assaulted in Trafalgar Square, central London.
The CCTV footage shows a man running before he is punched in the back of the head and kicked after he collapses on the floor.
The 50-year-old victim was assaulted outside the National Gallery, where he was later treated by London Ambulance Service , before being taken to hospital, where he remains in a critical but stable contition.
Police say no weapons were involved in the assault.
Detectives from Westminster Serious Crime Unit are investigating, and officers are keen to trace anyone who was in the area around the time of the incident.
Police are interested in tracing anyone who witnessed, filmed, or took part in the assault, or the events leading up to, or following the incident.
Two male suspects are believed to be involved in the assault.
The first is described as having a full beard, a top knot hair style, and was wearing a red t-shirt, dark trousers and light coloured shoes.
The second suspect was wearing a black jacket with a white emblem on the right shoulder, and white writing with a picture on the back.
He was wearing a white top under the jacket, dark trousers and dark shoes with white soles.
No arrests have been made and enquiries into the incident continue.
Anyone with information relating to the incident, is urged to contact Westminster Serious Crime Unit on 07500 766462, or Tweet information via @MetCC.
Those wishing to pass on information anonymously, can do so by calling Crimestoppers on 0800 555 111 or visit crimestoppers-uk.org.
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