The 77-year-old singer has sued the BBC over coverage of the raid - which followed a sex assault allegation.
Sir Cliff, who denied the allegation and was not charged with any offence, says he suffered "profound and long-lasting damage" as a result of coverage.
BBC editors have said they will "defend ourselves vigorously".
Mr Justice Mann on Thursday began overseeing a trial, expected to last 10 days, at the High Court in London.
A barrister leading Sir Cliff's legal team told Mr Justice Mann 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 did not give any indication of the amount Sir Cliff wanted.
But Mr Justice Mann heard that the singer had already agreed to accept a £400,000 payment from the force which carried out the search.
Sir Cliff, who was abroad when the raid took place, had initially sued the BBC and South Yorkshire Police.
Mr Justice Mann was told in May 2017 how that dispute had been settled after the force agreed to pay the singer "substantial" damages.
The judge has now been given the figure by lawyers representing the force at the trial.
They explained in a written statement given to the judge how the force had in May 2017 agreed to pay Sir Cliff £400,000 and to pick up some of his lawyers' bills.
"We think it is hard to imagine a case of publicity about a suspect in a police investigation which could have caused greater damage to the autonomy and dignity of the claimant," said Mr Rushbrooke.
"When you look at the prolonged impact it had upon Sir Cliff's life."
He added: "We say this is a claim for an award at the very top end of the scale."
Lawyers have told Mr Justice Mann how in late 2013, a man made an allegation to the 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".
"In a nutshell, it is Sir Cliff's case that the BBC's coverage of the search was an invasion - indeed a very serious invasion - of his privacy for which there was no lawful justification," Mr Rushbrooke told the judge.
"The fact and the details of the investigation which the BBC published to the world at large, along with the video footage of his apartment being searched, were private information and there was no public interest in the disclosure of this information to the millions of viewers and website readers around the world to whom it was published.
"For strong public policy reasons, persons who are under investigation but have not been charged with any offence should not be publicly named other that in exceptional circumstances - circumstances which were not present in this case.
"Moreover, even if there had been some public interest in the fact that the claimant was under investigation, the way that the BBC went about publishing the 'story' was so disproportionate, and so intrusive, as to render it unlawful."
He said Sir Cliff was entitled to "very substantial" damages or compensation to reflect the "flagrant way" the BBC went about "breaching his rights".
Mr Rushbrooke said the BBC had used a helicopter, said the broadcasts and other publications were on any view "hugely intrusive", and spoke of "massive, massive coverage".
He added: "It is hard to encapsulate in words the sense of panic and powerlessness that must have been induced in him on August 14 2014 when he realised that the BBC were relaying instantaneously and indiscriminately around the world highly sensitive and damaging information concerning himself - all based upon an allegation of serious criminal conduct which he knew to be entirely false."
Mr Rushbrooke said Sir Cliff had been left with "no option" but to take legal action and told the judge: "What we are talking about is using TV cameras to spy into someone's home at the time when their target is in the most vulnerable position imaginable and then serve it up to the British public as the most sensational story imaginable."
He went on: "The coverage had a profound and continuing impact on upon almost every aspect of his life."
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