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Gravesham council has warned residents against bogus callers after reports people have had their bank details requested from someone claiming to be from the authority.
The council moved to reassure residents today following similar scams across the country.
Callers are phoning residents to tell them the council tax has been overpaid before asking for bank details to pay a refund.
A council spokesman said: "No one from the council will ever call to request bank details under any circumstances.
"We advise anyone who receives one of these calls to report the matter to the police and under no circumstances divulge any bank account details."
The warning comes on the same day Kent County Council's Trading Standards issued an alert against rogue traders following a series of incidents, including in Gravesend.
This week alone, more than £11,000 has been demanded in payments from cold calling in Gravesend, Swanley, Maidstone and Cranbrook.
Residents have been warned to remain vigilant about anyone calling their home offering to carry out any work.