The 77-year-old singer is suing the corporation over its coverage of a police raid of his apartment in Sunningdale, Berkshire, which his lawyers argue caused “profound and long-lasting” damage to him.
During a preliminary hearing on Thursday, Mr Justice Mann said journalists could fairly argue that Sir Cliff’s personal finances should not be kept from the public simply because he wants them to be.
However, he did assure the star’s representatives that documentation containing such information would remain private for now.
“It does not follow that these matters will remain confidential at the trial,” he said.
“An argument could be made that these arguments should not be held in complete secrecy simply because (Sir Cliff) wants to keep his financial affairs secret.
“It should not be assumed in any way that these matters will remain confidential during the trial.”
Justin Rushbrooke QC, who is heading Sir Cliff’s legal team, has insisted his client’s financial information should be protected by the court.
The raid covered by the BBC in August 2014 was related to an allegation of sexual assault made to Metropolitan Police against Sir Cliff the previous year.
The star’s accuser claimed he had been assaulted as a child at Sheffield United’s Bramall Lane stadium in 1985.
The allegation was passed to South Yorkshire Police in July 2014 and – with Sir Cliff having denied the claim – prosecutors announced that no charges would be broughtin June 2016.
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Sir Cliff – who was not at the hearing on Thursday – received substantial damages from South Yorkshire Police after suing the force, but any trial regarding his case against the BBC will not take place until next year.
BBC editors have said they will ”defend ourselves vigorously”, with a spokesman adding that the corporation had reported the performer’s ”full denial of the allegations at every stage”.