Lawley, who became only the third host of the 64-year-old programme when she joined in 1987, told station controller Mark Damazer a fortnight ago that she wanted to leave and will present her last show in August.

The BBC has not identified a replacement, but choosing Lawley's successor will prove difficult for Mr Damazer.

The programme is one of the station's best-loved institutions - with 1.78 million listeners, according to the latest Rajars, its best audience for seven years - and Radio 4 listeners are notoriously protective of "their" station.

Listeners kicked up a huge furore recently when Mr Damazer axed the station's UK Theme from its early morning broadcasts after 33 years.

"I told Mark Damazer a couple of weeks ago that I would like to give up the programme," said Lawley.

"I've had more than 18 very happy years and have talked to some extraordinary people as they revealed themselves through their choice of music.

"It is one of the best jobs in broadcasting. But it has dominated my professional life and I feel the time has come to concentrate on other aspects of broadcasting and maybe a bit of business too."

Lawley took over as host from Michael Parkinson, who had earlier succeeded the programme's creator, Roy Plomley, who presented the programme from its inception in 1942 until his death in 1985. But Lawley's appointment proved unpopular with Plomley's widow, Diana, who criticised her for quizzing guests about their sex lives.

In 1996 she famously grilled the then shadow chancellor, Gordon Brown, about his sexuality. However, Lawley was not fazed, saying: "I genuinely do not set out to make headlines. But once people have agreed to take part they have given licence for me to ask about all aspects of their lives."

Among the 750 A-listers cast away on Lawley's island - out of more than 2,600 since the programme began - have been Enoch Powell, Neil Kinnock, Arthur Scargill, Lord Hailsham, the Duchess of Kent, Dame Edna Everage, Eric Clapton and Joan Collins.

Mr Damazer said: "I tried hard to persuade Sue to change her mind but to no avail. She started her career as a journalist and is still a journalist at heart.

"She also has an enormous interest in people. Put these two attributes together and you end up with fascinating and entertaining interviews that are now the hallmark of Desert Island Discs. She will be a tough act to follow."

Lawley will broadcast her last Desert Island Discs on Sunday August 27.

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