A thief tricked his way into the home of a 94-year-old woman and stole £500.
The man claimed to be from the water board when he called at the house in Handsworth Avenue in Highams Park at 7am on July 28.
Police say there have been reports of five similar distraction burglaries in the borough over the last three months.
A spokeswoman said: "We would like to urge families and social workers to give more help and support to any vulnerable relatives and to ensure they know what to do when a stranger knocks on their door.
"Some simple crime prevention tip can be given such as always use a door chain so the door can be opened slightly and check through a spy hole or window before opening the door.
"Ask to be shown ID and take a good long look at it and don’t them just flash it in front of your. Call the company they claim to be from, or if you think they are not genuine call 999."
Police are yet to issue a description of the burglar.