Kara Noble, the former friend of Ms Rhys-Jones who sold that and other photographs to the paper, was sacked from her lucrative job as a radio disc jockey and condemned by her colleagues.
The Palace also announced that it was making a formal complaint to the Press Complaints Commission over the affair, and Downing Street offered thinly veiled support.
In the face of such a backlash, David Yelland, The Sun's editor for a year, made an abject climbdown. In a statement issued last night, he said: "An editorial expressing our regret will appear in tomorrow's Sun.
"We clearly upset Miss Rhys-Jones. It's clear to me that we have caused her great distress. I have therefore decided to apologise to her and to the Palace. I believe this is the right thing to do. No more topless pictures of Miss Rhys-Jones will appear in The Sun. I wish her and Prince Edward the very best, although I don't expect to be invited to the wedding."
The photograph, among several taken by Ms Noble during a Capital Radio business trip in 1988, showed the DJ Chris Tarrant lifting up Ms Rhys- Jones' bikini top while the two were in the back of a car. Mr Tarrant denied that there had ever been any improper relationship between them, and said that he had started legal action against the newspaper.
In a statement broadcast on his breakfast show yesterday, he also attacked Ms Noble.
"To the person who has sold these pictures, you know who you are. Kara, how will you ever be able to look Sophie in the face again? I don't feel angry, I don't feel disgust - I feel deeply saddened," he said.
Ms Noble, who is believed to have sold the pictures for pounds 40,000, was sacked from her job at Heart 106.2 FM, a London station where she presented the breakfast show. A spokesman for the company said she had brought its name into disrepute.
Richard Huntingford, managing director of Chrysalis Group, parent company of the station, said: "We are shocked and disappointed that Kara Noble has betrayed the trust of Sophie Rhys-Jones and everyone here at Heart 106.2. Her actions are completely at odds with everything that Heart, as a hugely popular, family-focused, radio station stands for."
A Downing Street spokes-man said: "Freedom of the press is very important but with freedom comes responsibility and it's important that when the media exercise that freedom you show judgement."
David Aaronovitch, Review, page 3Reuse content