At 12.10pm on Tuesday, September 4, a woman in her 40s found a man in her kitchen in Overcliff Road.
The man was believed to have gained entry after climbing over a rear fence and opening the back door.
Nothing was taken from the property and the woman was not injured.
The burglar is described as white, 5ft 2ins tall, aged in his late 30s to early 40s, of slim build, with a three-inch scar on his face.
He wore a distinctive bowler style hat, black t shirt and blue jeans.
A police spokesperson said: “This was a very strange incident whereby a woman found a strange man in her kitchen. She escorted the man off her premises and rightly contacted the police. We would like the public’s help in identifying him to prevent anyone else having a similar experience.”
Anyone with information is asked to contact Ds Steve Franklin at Grays on 101 or Crimestoppers anonymously on 0800 555 111.