The woman targets elderly residents and claims to be from the Salvation Army, in order to gain entry.
Police said she does not wear uniform.
Detective Constable Ian Dearling said: “On Thursday last week (May 31) we arrested a woman in relation to these offences. She was later released under investigation.
“However, we believe there may be other old age pensioners who have recently been victims of this type of crime but who have not yet come forward.
“We would like to hear from them or from anyone else who may have relevant information.
“They are asked to report details online or by calling Sussex Police on 101, quoting serial 1238 of 29/05.
“Alternatively, they can visit the Crimestoppers website or contact the independent charity anonymously on 0800 555 111.”
Meanwhile DC Dearling urged people to be vigilant and not to answer the door to strangers or unexpected visitors, while encouraging family, neighbours and friends of vulnerable people to keep an eye on them and to report anything suspicious without delay.