The BBC denied the allegation, Mr Justice Mann was told.
Sir Cliff has sued the BBC - and South Yorkshire Police - over reports naming him as a suspected sex offender.
BBC editors have said they will ‘’defend ourselves vigorously’’.
Detail of rival claims emerged at a preliminary hearing before Mr Justice Mann at the High Court in London on Wednesday.
The singer was not at Wednesday’s hearing.
Sir Cliff has taken legal action against the BBC and South Yorkshire Police in the wake of coverage of a raid at his apartment in Sunningdale, Berkshire, in August 2014.
Lawyers representing Sir Cliff said - in written submissions - in October that he had suffered ‘’profound and long-lasting’’ damage.
They say he has sold the apartment which was raided because the prospect of living somewhere which had been ‘’so publicly violated’’ distressed him.
They say the furore threw his ‘’creative and business plans’’ into disarray - and forced him to delay the release of an album of ‘’rock ‘n’ roll classics’’.
And they say he has run up more than £1 million in lawyers’ bills.
In December a BBC spokeswoman said bosses would defend coverage.
‘’As we have said on several occasions, we are very sorry that Sir Cliff Richard has suffered distress,’’ she said.
‘’However, we have now submitted our response to this claim and will defend ourselves vigorously.’’
She added: ‘’It is the BBC’s responsibility to report fully stories that are in the public interest. Police investigations into prominent figures in public life are, of course, squarely in the public interest.’’
The spokeswoman said ‘’at every stage’’ the BBC had reported Sir Cliff’s ‘’full denial of the allegations’’.
In June, South Yorkshire Police apologised ‘’wholeheartedly for the additional anxiety caused’’ to Sir Cliff by the force’s ‘’initial handling of the media interest’’ in its investigation into the singer.
A barrister representing Sir Cliff on Wednesday outlined differing stances taken by South Yorkshire Police and the BBC.
“South Yorkshire Police’s case is that they were effectively strong-armed into co-operating,” said Justin Rushbrooke QC.
“The BBC say not so. All (a reporter) did was to say he knew that (Sir Cliff) was being investigated by South Yorkshire Police.”
Mr Justice Mann has been told that in late 2013, a man had made an allegation to the Metropolitan Police, saying he had been sexually assaulted by Sir Cliff at a public event at Sheffield United’s Bramall Lane football stadium in Sheffield as a child in 1985.
Metropolitan Police officers had passed the allegation to South Yorkshire Police in July 2014.
Sir Cliff had denied the allegation ‘’as soon as it was brought to his attention’’ and in June last year, prosecutors announced he would face no charges.
He has alleged that the BBC made an agreement with South Yorkshire Police.
And he says South Yorkshire Police contravened guidance on “relationships with the media”.
The singer says his privacy was invaded and he wants “’very substantial” damages.