Footage shown to the jury showed a man leaping over the garden fence shortly before 4am then tiptoeing around and trying to open a door.
Later the owner of a nearby property, Daniel McFarlane, disturbed a burglar who left behind a hat, scarf and screwdriver.
Nothing was taken from either address, jurors were told.
Batton’s DNA was found on the hat and scarf.
A white jacket like the one worn in the Family Fox Cam footage was found by police at Batton’s home.
The covert camera was set up by Mr King, who also presents Big Cat Diary on BBC1, to capture footage for a show he was making about the life of urban foxes.
When the owner of the property noticed the camera had been activated overnight she handed the film to police, and it was used in connection with the later burglary in Herne Hill, South East London.
The footage was uploaded to YouTube by Simon King Wildlife soon after it was filmed in January last year.
Dominic Bush, prosecuting, told the court: “Police were called when Mr McFarlane realised he had been burgled.
“By sheer coincidence, a nearby property had cameras set up in the back garden to record night time wildlife.
"The owner thought there was a good chance she might have caught the burglar on camera.
“Sure enough, at 3.46am, the cameras could see the burglar coming over her fence. To get to there he must have climbed over a few properties.
"The burglar’s then gone to the neighbouring property where he left a hat and scarf. It is as plain as day the man in the dock is the man on the CCTV.”
Batton, of Lewisham, South East London, denies burglary and attempted burglary.
Trial continues at Woolwich crown court.