Two women in Surbiton and Hampton were contacted on Sunday by a man calling himself Dr Pritchard who claimed to work for Kingston and Richmond Health Authority.
He called them to talk about a new method of carrying out the tests and invited them to attend his clinic to have it carried out.
All GPs in the area have been contacted by the health authority, and the police have been notified.
A health authority spokesman
said: "Hopefully these are isolated incidents.
"Both people who have been contacted realised it was bogus and contacted us or the police."
Patients are asked to report any calls to police or Shelagh Eaton at the health authority on 020 8339 8081.
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