Sir Terence applied in July to register the name as a trademark, which he said was normal company policy to "protect ourselves against people who may wish to use these names to take advantage of our reputation".
But the two other restaurants with the same name in London, in Covent Garden and Lexington Street, have been operating for 30 years and five years respectively - rather than one month, as is the case with Sir Terence's restaurant in the Great Eastern Hotel in Liverpool Street.
Lawyers say the owners of the two restaurants have a legitimate claim to prevent Sir Terence's application because they have been operating for much longer. At least one of the restaurants has been advised to fight the application in court.
But Conran Holdings, Sir Terence's company, has hinted it will vigorously resist any court challenge brought by the other restaurant owners - even though Sir Terence admits in a letter to The Independent that he knew of the two Auroras when he chose the name.
The possibility of facing the might of Sir Terence's company has concerned the other restaurateurs. "We are a bit worried. There are all sorts of problems if this goes any further - we've been reviewed in restaurant books and so on, which means this will be very confusing if it goes ahead," said the owner of one of the Aurora restaurants who preferred to remain anonymous. The owner confirmed that lawyers had advised the restaurant to oppose Sir Terence's trademark application.
Bill Moodie, head of intellectual property at the international law firm Herbert Smith, said: "It sounds like quite a good little battle. If the other restaurants object and can show that they have used the name for some years, they could prevent him getting the trademark."
Tony Willoughby, a partner at Willoughby & Partners, added: "The others will no doubt oppose his application."
Trademarks are granted by the Trademark Office, which does not investigate whether a name is already in use by a rival, but simply whether the name is "distinctive".
Simon Brown, the finance director of Conran Holdings, said the company always tried to register the names of its restaurants to prevent people "passing off" their own properties as somehow being associated "We have taken action in the past, when in 1997 we found somebody was using the `Zinc' name to cause confusion," Mr Brown said. "People were turning up and finding that it was just a construction site."
Sir Terence insists that if he is granted the trademark, he "does not intend" to use it against the existing Aurora restaurants. "Even if we wanted to, it is most unlikely that we would be able to do so," he said. But that then calls into question the value of having the trademark in the first place.
Mr Brown said that the benefit would apply to the existing restaurants too, in that Conran Holdings could prevent newcomers from using the name. But he warned that if the existing restaurants challenged the trademark in court "it will cost them in legal fees".
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