The 77-year-old singer has taken legal action over coverage of a raid on his home following a sex-assault allegation.
BBC bosses dispute his claims.
Mr Justice Mann began overseeing a trial in London on Thursday. Sir Cliff is due to give evidence on Friday.
He was in court on the first day of the trial to hear lawyers’ submissions. Reporters asked how the day had gone as Sir Cliff left.
The singer replied “very good, thank you” and waved as he climbed into a taxi.
A barrister leading Sir Cliff’s legal team told Mr Justice Mann on Thursday that BBC coverage of the search at the singer’s apartment in Sunningdale, Berkshire, in August 2014 was a “very serious invasion” of privacy.
Justin Rushbrooke QC told how coverage had a “prolonged impact” on Sir Cliff.
He said the singer should get compensation at the “very top end of the scale”.
The BBC says its coverage of the police raid on Sir Cliff Richard’s apartment was accurate and in good faith.
Lawyers representing BBC bosses told Mr Justice Mann that the raid was a “matter of legitimate public interest”.
They said BBC reporting contributed to public debate.
Gavin Millar QC, who is leading the BBC legal team, said journalists had respected Sir Cliff’s rights as “the suspect” and “in particular the presumption of innocence”.
The trial is due to last 10 days.
Lawyers have told Mr Justice Mann how in late 2013, a man made an allegation to then Metropolitan Police, saying he had been sexually assaulted by Sir Cliff, during an event featuring evangelist Billy Graham 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 has said that the BBC had reported Sir Cliff’s “full denial of the allegations at every stage”.