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"Having tried exceptionally hard to make our relationship work given the daily pressures surrounding us, it is with sadness that we have decided to go our separate ways," the couple said.

"Our parting is amicable and both of us still care about each other very much but have found it increasingly difficult to maintain a normal relationship with constant intrusion into our private lives, and we have actively tried to protect the privacy of our child.

"Separation for any couple is difficult enough, but to have to go through this so publicly, especially with a small daughter, is immensely stressful. We hope, for the sake of our baby daughter, that we will be given some space and time to get through this difficult period."

Sir Paul is listed in the Guinness Book of World Records as the most successful songwriter in popular music history, with 29 US No 1 hits to his name, including 20 with The Beatles. He earned an estimated £48.5 million last year from music sales and a North American tour and has a fortune reckoned to total £825 million.

Lady McCartney has revealed in the past that she offered to sign a prenuptial agreement before marrying Sir Paul, to protect that fortune, but said that he turned her down. "I wanted to prove that I love him for him," she told Vanity Fair in 2002.

A leading UK divorce lawyer, Alan Kaufman of Finers Stephens Innocent, said Sir Paul must be regretting that decision now. He said: "This will be one of the biggest, if not the biggest, divorce cases to hit the English courts, if it gets that far.

"In recent cases wives have got more and more and have ended up with massive settlements. This area is a minefield. The courts have a very wide discretion. There are no hard and fast rules except that the wife is entitled to a ‘fair settlement’," he added.

The lawyer said that a case currently awaiting judgment in the House of Lords would have a significant impact on any eventual divorce settlement between the McCartneys.

A City fund manager, Alan Miller, is contesting a Court of Appeal ruling which awarded his wife Melissa a £5 million share of his £20 million fortune for a marriage which lasted less than three years.

Mr Kaufman, who handled the divorce of Julia Carling and several high profile rock stars, said: "My gut feeling is that the decision in Miller v Miller will be upheld, which means that Lady McCartney could be looking for something like £200 million. She may even try to get more."

He added: "Although we are not like America and most of Europe, where these things are binding, there are a number of precedents in which a pre-nup has been counted as a major factor in the English courts.

"It would certainly have given Sir Paul a much better shot and I bet he’s sorry now he didn’t have one."