The Royal Family last night fought back to limit the damage from the "Sophie tapes" affair after the Countess of Wessex stepped down as chairman of her public relations company.

The Queen gave her full support to Sophie and her husband Edward, the Earl of Wessex, in their desire to pursue working careers despite their status.

She hit out at the "subterfuge" used to obtain the recordings.

Sophie, 36, was duped by a fake Arab sheikh in a videotape "sting" by the News of the World, in which she made indiscreet remarks about senior Royals, leading politicians and current issues, including fox hunting and Chancellor Gordon Brown's Budget.

In a personal statement she said: "I am deeply distressed by the carrying out of an entrapment operation on me and my business, but I also much regret my own misjudgement in succumbing to that subterfuge."

She said she had discussed the situation with the Queen and had decided to step aside as chairman of R-JH while the issues raised by recent events were carefully considered.

"This has been a difficult time for me. I take very seriously the issues raised and, naturally, regret any embarrassment, above all to the Queen."

However it is believed Sophie, a director and shareholder in R-JH Public Relations, will continue to have a hand in running the business.

Co-founder Murray Harkin, 36, also resigned yesterday after he was recorded making damaging revelations about his personal life concerning sex and drugs.

He also called into doubt Edward's heterosexuality despite Sophie's insistence, in an authorised but highly criticised interview published last week, that Edward is not gay.

Jack Cassidy, formerly a non-executive director of R-JH, has been appointed acting managing director to succeed Mr Harkin who is "taking a complete break from business".

The Queen, in a separate statement, was said to deplore the "entrapment, subterfuge, innuendo and untruths" to which Sophie and Edward, 37, had been subjected.

New Palace guidelines would now be drawn up to regulate how "working Royals" conducted their business lives to ensure they could not make money from exploiting their royal position.

"Her Majesty accepts that despite the difficulties of recent days, both the Earl and Countess understandably want to try to pursue working careers and they have her full support in doing so," said the Palace.

"It is not an easy option and they are breaking new ground, but it is right in this day and age that they should be allowed to do so."