UPDATE: Police have since found a body in the River Thames.
A spokesperson for the Met said:
"At 07:07hrs on Tuesday, 18 August, police were called to reports of a body seen in the River Thames at Putney Bridge.
"The Met’s Marine Policing Unit attended and recovered the body of a man from the water.
"Although formal identification awaits, police believe that the deceased is Paul Conte.
"The death is currently being treated as unexplained."
The Met added that Paul's next of kin were being supported by specialist officers.
SEE MORE: Body found in search for missing south London man
Police are looking for a Putney man who went missing last weekend after a house party in Barnes.
Paul Conte, 21, was last seen in SW13 at around 12:40am on Sunday, 15 August.
The young man is thought to have been wearing a white t-shirt, black jeans, white shoes and had his hair tied in a bun. He is 5ft 10ins and of slim build.
He had been to a party in Ferry Road, Barnes, SW13 on the evening of Saturday, 14 August and left in the early hours of Sunday morning at approximately 12:30am.
He was captured on CCTV in Galata Road, SW13 at 12:35am and at 12:38am on Parke Road, SW13.
At this time police believe he should have walked through the Barnes area on his way home, and he would have been expected to arrive approximately one hour later.
Paul has not been heard or seen from since, and officers are growing increasingly concerned for his welfare.
They are urging residents to check their doorbell footage to see if there is any sighting of Paul.
Sergeant Amy Everitt, of the Met’s South West Missing Persons Unit, said: “Paul’s disappearance is completely out of character and we are growing increasingly concerned for his welfare.
“Officers are working hard to find him and, we very much want to hear from anyone who has been in contact with him, or may have seen him in the Barnes area at around the time he was last seen. If you live in the Barnes area, especially the roads around Ferry Road, SW13, please check any door bell footage you may have to see if you captured any images of him.
“Please do contact us if you have any information that might help us find him.”
Anyone with information to call 999 quoting reference 3655/15Aug. You can also contact the Missing People charity anonymously by calling 116 000.
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