The Princess, who condemned the photographs published in the Sunday Mirror and Daily Mirror as 'gross intrusion', is also asking for them to be kept in a safe place and for details of profits made from their sale.
This would force Bryce Taylor, owner of the LA Fitness Club where the pictures were taken, to disclose how much he was paid and the Mirror Group to reveal profits from increased sales. This could form the basis for a damages claim although the case is unlikely to go to court.
The writs were served on Mirror Group Newspapers, David Banks and Colin Myler, the editors of the two newspapers that published the photographs, the club in Isleworth, west London, and Mr Taylor.
The Princess is claiming that the newspapers, the gym and its owner breached confidence. The LA Fitness Club and Mr Taylor are alleged to have breached her membership contract and the Mirror Group and its editors are said to have induced that breach. The writs were served on the Mirror Group yesterday.
Representatives of Network Security Management Ltd, hired by the Princess's solicitors, were unable to find Mr Taylor, and last night handed the writ to his public relations adviser, Max Clifford.
Mr Clifford denied that Mr Taylor was 'cutting and running', but said he was flying to New Zealand to visit his mother for Christmas.
If the defendants agree to the terms laid down in the writs within 14 days, that will end the matter. Otherwise their lawyers must lodge an 'acknowledgement of service' with the High Court stating whether they will contest the case.
If they do not respond, the Princess can apply for summary judgment. The writs make no mention of damages but seek 'further or other relief' and ask for the plaintiff to be awarded costs.
On Monday, the Princess was granted a temporary injunction preventing further publication of the photographs taken by a secret camera at the gym. If the case does go to court, one of the main issues would be the terms on which the Princess joined the pounds 475-a-year club.
Unless she was specifically guaranteed protection against intrusion of privacy, it would have to be decided whether there was implied confidentiality and whether that was breached.
Although the Mirror Group has remained defiant in the face of condemnation of the publication of the photos, Mr Banks, editor of the Daily Mirror, yesterday admitted that he and Mr Taylor could be described as 'ratbags'.
In an interview with an Australian network replayed on BBC Radio, he admitted that Mr Taylor's action in secretly photographing the Princess was 'a particularly sneaky trick, frankly, and the bloke who did it has got to go down as one of the ratbags of the year'.
He argued that once the pictures had been taken there was no reason why they should not be used, but admitted: 'I don't exclude myself from a scale of rat-baggery, but I would give him a nine and I'd come in at a seven, I think.'
The Daily Mirror claimed last night that other newspapers had promised to end their criticism of its use of the pictures.
The Press Complaints Commission is due to meet today, but will not be discussing the use of the pictures because the matter is 'sub-judice', Lord McGregor, the commission's chairman, said.