The force was alerted to reports of a body in the Thames near Embankment, central London by the Royal National Lifeboat Institution at 11.51am on Tuesday.
Officers from the Met’s marine support unit recovered the body.
Detective Chief Inspector Lucy O’Connor, of the Central South Command Unit, said: “We are providing Harvey’s family with all the available information.
“We are also asking for media to please respect the family’s privacy at this challenging and difficult time.”
CCTV footage showed Mr Parker walking into Craven Street and then south towards the Embankment, and he has not been seen since.
A friend said the University of York music student had been to a Little Simz concert in Brixton, south London, before going to the nightclub.
On Wednesday, the Metropolitan Police said that investigators had viewed CCTV near the Golden Jubilee Bridge and believe Mr Parker, who is a member of front of house staff at the Theatre Royal Stratford East, may have entered the water there.
The force said that there was nothing to suggest anyone else was involved.