Its lawyers have told a preliminary High Court hearing that the singer has run up "disproportionate" legal costs of more than £500,000.
He is suing the BBC and South Yorkshire Police over coverage of the 2014 raid.
Lawyers for Sir Cliff previously said he had suffered "profound and long-lasting" damage from the incident.
He was investigated over historical sexual assault allegations, which he denied, and the case was dropped by the Crown Prosecution Service in June last year because of insufficient evidence.
He is seeking "very substantial" compensation because he says the coverage invaded his privacy.
If Sir Cliff's claim succeeds, and he wins damages, the BBC could be ordered to cover all of his lawyers' bills.
A spokesman for the singer said he had "incurred these costs and expenses over more than a two-year period, we say as a direct result of the actions of South Yorkshire Police and the BBC.
"Ultimately it will be down to a judge to decide whether or not he should recover such costs and expenses in full or in part, or at all."
Lawyers representing the BBC criticised the singer's legal costs as a judge analysed the latest stage of the dispute at a High Court hearing in London on Thursday.
Sir Cliff was not at the preliminary hearing, which is due to end on Friday, before a planned trial.
Details of the singer's claim emerged last year in paperwork lodged at the High Court.
His lawyers said in October that he had suffered "profound and long-lasting" damage from the BBC's live coverage of the search at his apartment in Sunningdale, Berkshire, in August 2014 and from being publicly named as a suspected sex offender.
They also say South Yorkshire Police contravened guidance on "relationships with the media".
BBC editors have previously apologised for distress but have said they will "defend ourselves vigorously".
Speaking in December, a BBC spokeswoman said the broadcaster had reported Sir Cliff's "full denial of the allegations at every stage".
In June, South Yorkshire Police apologised "wholeheartedly for the additional anxiety caused" by the force's "initial handling of the media interest" in its investigation into the singer.
Sir Cliff Richard has spent "grossly unreasonable" amounts on lawyers after taking legal action over coverage of a police raid on his home, the BBC says.