Darren February, 34, of no fixed address, denies taking valuables from an open safe on 4 December 2015.
The X Factor judge was asleep in the property with his partner Lauren Silverman, their son Eric and a nanny at the time of the break in.
Isleworth Crown Court heard Mr February had dozens of burglary convictions.
Items worth £950,000 were taken from a safe inside a wardrobe which had been left open because Ms Silverman was due to travel the next morning.
Prosecutor Denis Barry told the jury Mr February had first tried the front door of the house in Holland Park, in an attempt described in court as "a bit ambitious".
Mr Barry said: "It would appear from the CCTV that the burglar is catching his breath because he had to shimmy over lots of different walls to get in to the premises and around the premises."
Mr February was identified by two police officers who studied CCTV footage, Mr Barry said.
The prosecutor added: "Mr February over a few years has committed a total of 37 burglaries and what is more relevant, he has committed a total of 37 burglaries, most of which are in this area."
Mr February denies one count of burglary.
The trial continues.
A burglar scaled several walls to break into Simon Cowell's west London home and steal jewellery worth almost £1m, a court has heard.