Jemima Khan described weekend rumours that she has taken out a gagging order preventing "intimate photos" of herself and Jeremy Clarkson being published as a "bloody nightmare".

The socialite was among a number of celebrities alleged to have taken out privacy injunctions to stop potentially embarrassing details being made public. A Twitter account claiming to expose the celebrities has attracted about 30,000 followers since its first message on Sunday afternoon.

Khan said the rumours were "untrue and upsetting", and added on Monday: "I hope the people who made this story up realise that my sons will be bullied at school because of it. Plus I'm getting vile hate tweets."

Khan has consistently denied having obtained a gagging order. On Monday, Mark Stephens, a senior media lawyer at Finers Stephens Innocent, told the Guardian: "This is discriminatory justice: not one single woman has sought or obtained a superinjunction."

Stephens added that the Twitter user behind the allegations "should expect a knock on the door within the next 48 hours" from solicitors representing the stars. "If it is false, it is libellous; if it is true, it is contemptuous," he said.

The lawyer added that anybody acting for the celebrities could attempt to force Twitter to hand over information about the person behind the account.

"Twitter can reveal the user who dialled up to the connection at that time," he told the Guardian. "The technical trail is indelible – it has the fingerprints of the miscreant all over it. They should expect a knock at the door in the next 48 hours and they should take their toothbrush to court, because they can expect to spend a very long time in Pentonville [prison]."

Privacy injunctions – and the high-profile figures alleged to have obtained them – have been thrown into the spotlight in recent weeks as MPs warn of a new privacy law created by judges, rather than parliament.

The use of Twitter and other internet sites to publicise the alleged injunctions has made the high court gagging orders "increasingly untenable," Stephens said on Monday. "We're in Spycatcher territory here. Eventually, the House of Lords will be forced to accept that the purpose of an injunction has been removed so remove it – as I'm sure they will on this occasion."

Twitter had not returned a request to comment at the time of publication. On Sunday, a Twitter spokesman said the company "strive[s] not to remove tweets on the basis of their content," but that it would remove "illegal tweets and spam".

Keith Arrowsmith, the head of intellectual property and media at Ralli solicitors, told the Guardian that superinjunctions – where even the existence of a gagging order cannot be reported – are rendered ineffective without an international "supercourt" to implement them. "Anything the government says about privacy law is now nonsense, because they can only tweak UK law."

Meanwhile, Helen Wood, a former escort who had previously been linked to Wayne Rooney, was interviewed on Monday by Victoria Derbyshire on Radio 5 Live, discussing the latest in the legal storm. A married actor, who allegedly once had a sexual relationship with her, has taken out an injunction preventing his identification.

She said that gagging orders allow the rich to "do what the hell you like" while having their reputation protected by the courts.

"They can behave exactly how they want to behave with who they like and so long as they have got a hell of a lot of money, they can go and protect themselves, and that is setting a bad example," she added.

You can listen to the full interview here:

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