The man, who wears a fisherman's black hat, has been linked to up to 450 burglaries in southwest London, including the home of Boris Becker.
He is said to enjoy "the notoriety of targeting the wealthy" and has stolen jewellery worth Â£10m over 12 years.
Premier League footballers have also been targeted.
Most of the stolen items have never been recovered, said police.
Three homes have been targeted in Wimbledon Village in the last two weeks by the suspect who often removes or destroys security equipment before breaking in.
Det Insp Dan O'Sullivan said: "This man has been linked to as many as 450 burglaries and related offences, making him the most prolific burglar in the UK over the past 12 years, and possibly in Europe.
"We are renewing appeals and asking for the public's help in identifying this man so that we can bring him to justice and bring his crime spree to an immediate halt.
"Someone must recognise this man and his distinctive clothing. He spends a lot of time away from home in the early hours, which cannot go unnoticed by his family and friends."
Officers said there have been two instances where CCTV systems at other residential properties in the area have been tampered with.
Speaking to BBC Radio 5 Live the detective said the suspect, dubbed the Wimbledon Prowler by the press, always kept his hand over his mouth to protect his identity.
Mr O'Sullivan said money was not his main motive, rather, "the notoriety of targeting the wealthy," including premiership footballers and Boris Becker's family who have been targeted twice in the recent past.
A burglar who targets the homes of the rich is being described by the Met Police as the most prolific in the UK and "possibly in Europe".