But others were appalled by the Duchess's behaviour and said a code of conduct for the Royal Family was also needed.
In a short statement, understood to have been authorised by the Queen, Buckingham Palace said: 'We strongly disapprove of the publication of photographs taken in such circumstances.'
The Daily Mirror defended its decision to publish seven pages of pictures, saying they 'strip away all the lies, humbug and hypocrisy that have surrounded the Duchess's relationship with Mr Bryan'.
More photographs of the couple on holiday were published in today's issues of the Daily Mirror, Sun and Today.
John Townend, Tory MP for Bridlington, said yesterday: 'This sort of thing does undermine the Royal Family. But it does prove the need for a privacy law.'
David Mellor, Secretary of State for National Heritage, who was pursued by the press over his affair with an actress, will face pressure for a privacy law on reporting of the Royal Family at the Conservative Party conference.
But Sir John Wheeler, former chairman of the Commons select committee on home affairs, said: 'If a married woman chooses to disport herself with another male under circumstances which she finds embarrassing, she has only one person to blame and that is herself.'
Lord McGregor of Durris, chairman of the Press Complaints Commission, said publication of the photographs did not strengthen the case for a privacy law. 'Everybody who has discussed the desirability of a law of privacy, from the Younger Committee of 20 years ago to the last royal commission and the Calcutt Committee two years ago, has recommended against it precisely because the advantage of protecting the privacy of private persons will inevitably result in protecting the misbehaviour of public persons.'
Lord McGregor said he had twice refused a request from Mr Bryan's solicitors to interveneto prevent publication.
Clive Soley, the Labour MP introducing a Bill to tighten controls on press accuracy, said the furore over the photographs and the Commission's failure to act would strengthen Tory support for his Bill.
He said: 'The Tories will be fuming about it. A lot of Tories have told me they are angry with Fergie for undermining the Royal Family because the Royal Family has always survived by remaining remote. Now they are showing their tits on the front page, they will be appalled. Queen Victoria wouldn't like it.'
The affair will revive demands for Civil List payments, now costing taxpayers nearly pounds 10m a year, to be limited to more immediate members of the Royal Family.
Labour MPs want to reopen the debate after being thwarted in their attempts to raise the issue in the Public Accounts Committee. They found the payments had been settled for a decade by the Government.
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