They claim her husband, thought to be of Greek origin, asked local shop owners if they had seen her when he awoke on the beach and noticed she was gone.
He reportedly told them that she had previously disappeared in London in 2020 after being sacked from her job and was subsequently found by police.
Lifeline Hellas, a Greek missing persons charity, issued an alert after the police were unable to find Bourda.
The charity’s alert said: “Her life is in danger. If you know anything, contact the Silver Alert service, 24 hours a day, at the national SOS line 1065.”
Bourda is described as having straight blonde hair down to her shoulders and hazel eyes, and as being 5ft 6in tall and of slim build.
The Hellenic Coastguard is reportedly conducting a search operation at sea and investigating reports that her belongings were left on the beach.
The British embassy in Greece shared a notice on Facebook which read: “Michele Ann Bourda went missing on August 1, 2025 at the beach of Ofrynio near Kavala.
“On the day she went missing, she was wearing a swimsuit with decorative stones, yellow water shoes and red plastic sunglasses. Her life is in danger.”
Last month, a 60-year-old British tourist went missing while on holiday in Greece.
He was last seen in Tristomo, a village on the island of Karpathos, and his car was abandoned in 38C heat.