John McIntyre reports: The Sun prints a full page apology

In an editorial in Thursday's paper headlined "Sorry, Sophie" editor David Yelland says the paper was "holding its hands up" to a mistake.

Mr Yelland, who has been in the job for nearly a year, says in the article: "We thought we were printing a saucy, but harmless, picture of Sophie Rhys-Jones.

"We thought it showed the fun-loving side of a woman who is bringing a breath of fresh air to the royals."

But The Sun admits it got it wrong and Mr Yelland says: "We clearly upset Miss Rhys-Jones. It's clear to me that we have caused her great distress."

He denied the paper had acted with "deliberate cruelty", as alleged by the Palace, and said: "We all make mistakes."

The BBC's Torin Douglas: The Palace still wants the Press Complaints Commission to consider the matter

The paper - which sells more copies than any other UK title - promised to write to " a private letter" to Miss Rhys-Jones.

Mr Yelland added: "I wish her and Prince Edward the very best, although I don't expect to be invited to the wedding."

The apology was accompanied by a cartoon which suggested that the Sun felt the Palace had over-reacted to the picture.

The Sun pioneered topless pictures in the 1970s and on Thursday its "page three girl" was called ... Sophie.

Radio and TV presenter Chris Tarrant, who was furious about the publication of the picture of himself with Miss Rhys-Jones, described the apology as "the biggest and fastest climbdown" ever.

Chris Tarrant: It was 'the biggest and fastest climbdown ever'

"It was appallingly cruel for Sophie and Edward," he said on Capital FM. "These are two harmless people completely in love due to marry in three weeks time. I said it yesterday - leave them alone, give them a chance."

Formal complaint

Buckingham Palace made a formal complaint about the publication of the picture to the Press Complaints Commission (PCC) only hours after Wednesday's Sun hit the streets.

Sun widely condemned

Prince Edward's fiancée was snapped topless with Mr Tarrant while on a business trip to Spain in 1988.

The Palace condemned the publication of the picture as "premeditated cruelty", and made the complaint under section three of the industry's code of practice, regarding privacy.

Earlier, a Palace spokesman said: "This morning's story in The Sun is a gross invasion of privacy and cannot be regarded as in the public interest.

"It has caused considerable distress. Prince Edward and Miss Rhys-Jones are very grateful to those members of the public who have telephoned offering support, which naturally is also our immediate concern."

Miss Rhys-Jones is reported to have been devastated by the publication of the photo and stayed away from work on Wednesday.

'Justify this intrusion'

PCC spokesman Luke Chauveau said The Sun would be asked to justify the picture and accompanying story.

Kara Noble: Sacked

He said: "We will be getting the publication to justify their intrusion into the individual's private life."

Kara Noble, a disc jockey was sacked from London commercial radio station Heart 106.2 after the photo was published.

Ms Noble was Mr Tarrant's co-presenter and a friend of Miss Rhys-Jones when the picture was taken nearly 10 years ago.

Prime Minister Tony Blair joined the Palace in its condemnation.