Mr Justice Lightman heard submissions in camera at the High Court in the Strand. Mr Bunn's solicitors, Burton Copeland, issued a writ on his behalf on Wednesday against the BBC and Victor Gollancz, publishers of the book Fraudbusters: The Inside Story of the Serious Fraud Office by Mark Killik.
Mr Bunn's writ applied for an injunction stopping the programme and book from revealing information given by him to the SFO which Mr Bunn claims was given in confidence.
Mr Bunn was the finance director of the private companies owned by Robert Maxwell. Mr Maxwell drowned after falling off his yacht in November 1991.
The book Fraudbusters was officially published yesterday and is already in the shops. It details the history of the SFO, which was set up in April 1988.
The book recounts how, after early successes in the Guinness and Barlow Clowes trials, the SFO ran into a storm of criticism following the collapse of the second Guinness case, the acquittals of George Walker and Kevin Maxwell, the release on appeal of the County NatWest defendants and the sentence of 180 hours' community service given convicted fraudster Roger Levitt.
The SFO is a revolutionary institution in that, for the first time, it brought together police, lawyers and investigative accountants in one body.