Bogus gas and water board officials have been targeting homes in Brighton and Peacehaven to carry out distraction burglaries.
A man called at the home of an 87-year-old woman in Stanstead Crescent, Woodingdean, at about 4.45pm on Monday (23 May).
He told her that he was from the gas company and that there had been an explosion.
They said that he needed to run her tap to check for contamination.
Nothing is believed to have been taken.
An hour later two men called on a 61-year-old woman in Arundel Road, Peacehaven, and claimed that the water supply may have been contaminated after a gas explosion,
Detective Inspector Rob Morland, from Sussex Police, said: “Taking advantage of the elderly and vulnerable is deplorable.”
He said that similar incidents had been reported in Haywards Heath and Hailsham.
He said: “I am keen to speak to anyone who witnessed anything suspicious in these areas or who may have had a similar visitor claiming to be from a utility company.
“I would like to remind residents to take your time when a visitor calls by.
“Use the door chain and thoroughly read and verify their identification.
“They do not need to be let in while you ring and check who they are.
“Remember, a genuine caller will always be happy to wait.”
The suspect from the Brighton burglary is described as white, aged in his thirties, 5ft 6in tall, slim and with short black hair, possibly gelled.
He was wearing a long-sleeved smart white shirt with the cuffs done up, a black or brown waistcoat over the top, buttoned up, black or brown smart trousers and smart shoes.
The first suspect from the Peacehaven burglary is described as white, aged 30 to 40 years old, slim, 5ft 8in tall and with dark hair.
He was wearing dark, navy coloured clothing.
The second suspect was described as white, aged in his forties, of a slightly sturdier build and taller, with dark hair and wearing a maroon coloured T-shirt.
Police are conducting house-to-house inquiries and forensic examinations.
Anyone with information is asked to contact Sussex Police on 0845 6070999 or the independent charity Crimestoppers anonymously on 0800 555111.