British diet guru and TV personality Michael Mosley was found dead on Sunday on the Greek island of Symi where he went missing this week, police said.

"People on a boat saw a body close to the rocky coast," said Petros Vassilakis, police chief for the southern Aegean region.

The lifeless body was spotted by a television crew from Greece's ERT public channel out filming in the area where the 67-year-old disappeared.

A cameraman "saw something strange near the fence, 50 metres from the sea," ERT reporter Aristides Miaoulis said on air.

"We discovered it was this man... he was lying down (on his back)."

Symi's mayor Lefteris Papakalodoukas was also with the crew and confirmed they had found Mosley, who had been vacationing on the island.

"It's the body of the journalist that we have been looking for over several days," he told ERT. The authorities had on Friday announced they were stepping up the search after the Briton was last seen alive on Wednesday.

His wife Clare Bailey alerted police that evening when he failed to return from a coastal walk on his own.

Papakalodoukas said Symi has been baking under "insufferable heat" and the area where Mosley was last sighted was "difficult because it's very rocky."

Much of Greece has seen record temperatures for the first week of June, reaching 39.3 degrees Celsius on Symi, which is close to Rhodes and western Turkey.

Tom Watson, a former deputy leader of the UK's main opposition Labour party who lost weight with the help of one of Mosley's books, paid tribute to a "hero" who produced "courageous, science-based journalism."

Mosley's co-presenter on the BBC program "Trust Me, I'm A Doctor," Saleyha Ahsan, told BBC News he had a "passion" for making science "accessible to anyone and everyone."

Mosley trained as a doctor after working as an investment banker and joined the BBC as a trainee producer.

He went on to make science and history documentaries and in the past decade carved out a niche as a health guru in front of the camera and as the author of best-selling diet books.

The health journalist, credited with popularising the 5:2 intermittent fasting diet, appeared on TV programs including "The One Show" and "This Morning." (AFP)