Thirsk crash: Firefighter dispatched to scene of fatal collision found his own son among injuredHe has sued the BBC over coverage of a police raid, at his apartment in Sunningdale, Berkshire in August 2014, follow an allegation of sex assault.
The 77-year-old singer, who denied wrongdoing and was not charged with any offence, says he suffered "profound and long-lasting damage" as a result of coverage and wants damages. BBC editors have said they will "defend ourselves vigorously".
A judge is due to oversee a trial in London in April.
Mr Justice Mann on Thursday oversaw a preliminary hearing at which he analysed a dispute over whether some information contained in witness statements gathered by the BBC should be allowed to emerge at the trial.
The judge said the information should stay under wraps for the time being, but he said he would review rival arguments during the trial.
Sir Cliff's lawyers said the information at the centre of the dispute was sensitive and private and should not be aired at the High Court trial.
But lawyers representing BBC said bosses would not agree to the evidence being withheld or not referred to in open court proceedings.
They said the information was "important and significant" to their case and said any "derogation from open justice" had to be "strictly necessary".
Justin Rushbrooke QC, who is leading Sir Cliff's legal team, said five "sensitive" passages in witness statements contained information about the police investigation into the singer which was not in the public domain.
"What is contained within the paragraphs of these witness statements is plainly within the four corners of what we say is private information," he told the judge.
"This is the BBC holding itself up as the guardian of the public interest and saying the public is entitled to hear its full evidence."
He added: "It is plainly wrong to say they will get any less a fair trial from your Lordship if these passages, five in all, are withheld from public inspection."
Mr Rushbrooke said Sir Cliff was not asking the judge to sit in private.
Gavin Millar QC, who is leading the BBC's legal team, said the passages should be aired in open court.
"The passages in these witness statements are not part of an attack by the BBC," he said.
"These passages are there as part of the BBC's case."
He added: "We don't say we are the guardian of the public interest."
Mr Millar said the open justice principle should apply.
Lawyers have told how, in late 2013, a man made an allegation to then Metropolitan Police, saying he had been sexually assaulted by Sir Cliff at Sheffield United's Bramall Lane football stadium in Sheffield when a child in 1985.
Metropolitan Police officers passed the allegation to South Yorkshire Police in July 2014.
Sir Cliff denied the allegation and in June 2016 prosecutors announced that he would face no charges.
A BBC spokesman said the BBC had reported Sir Cliff's "full denial of the allegations at every stage".
A spokesman for Cliff Richard said: "Sir Cliff wishes to make it clear that the few short passages that will be removed from the public versions of the witness statements simply contain details of the false allegation that gave rise to the police investigation which are not already in the public domain.
"Although the allegation is false, and did not lead to any action being taken by the CPS, it is something which has caused him a great deal of emotional trauma and pain, which is ongoing.
"The BBC made it clear that they were not suggesting that that allegation was true and that those details had not been put in the statements for that purpose.”
Judge should know Sir Cliff Richard's cash settlement with police - BBC
BBC bosses want to tell a judge how much Sir Cliff Richard pocketed when he settled a damages fight with a police force.
The singer originally sued the BBC and South YorkshirePolice.
Mr Justice Mann was told in May 2017 that the dispute with South Yorkshire Police had settled after the force agreed to pay the singer "substantial" damages.
But the judge says he does not know the figure.
BBC bosses say they know how much Sir Cliff was given and want to tell the judge.
Lawyers say the figure is a "material factor" and the judge needs to know.
Sir Cliff says he does not consent to Mr Justice Mann being given the figure.
The singer's lawyers say such knowledge could influence Mr Justice Mann's assessment of the amount of damages he might order the BBC to pay.
Mr Justice Mann said he would make a decision on whether he should be told at a later date.