South Yorkshire Police's David Crompton was being questioned by the Commons Home Affairs Committee into the row over a leak to the BBC before last month's raid in Berkshire.
The officer said the force had been "fatally compromised" by what he said was a leak from Scotland Yard's Operation Yewtree sex abuse investigation. He said the force made a deal with the broadcaster after it had approached it with detailed information about the planned inquiry.
He said: "The problem is that investigation could never be done in a low-profile way because it was fatally compromised from the outset."
Committee chairman Keith Vaz MP asked: "By Operation Yewtree?" and Mr Crompton replied: "Yes."
Mr Crompton added: "We were placed in a very difficult position because of the original leak and the BBC came to us knowing everything we knew, as far as the investigation was concerned.
"My concern was that if we showed the BBC the door, the very clear impression which had been left with my staff in the media department was they were likely to publish the story. That would have impeded our investigation.
"I'm confident we made the right decision in difficult and unusual circumstances."
Mr Crompton denied Mr Vaz's suggestion the BBC had blackmailed him, but added: "It put us in a very difficult position."
The force has complained to the BBC about its coverage of the search last month, claiming an analysis piece posted on the broadcaster's website was an attempt to distance itself from what had happened.
Mr Crompton said: "The coverage was disproportionate and made our actions look heavy-handed and intrusive. I regret that."
The police chief confirmed he did not approach senior BBC management to ask them not to run the story.
Mr Vaz said he was "amazed" by "what appears to be the sheer incompetence with the way in which this matter was dealt with. He also referred to Mr Crompton's failure to phone the Metropolitan Commissioner over the alleged Yewtree link.
BBC director general Lord Hall later told the Committee that if senior editorial staff had been approached by the police warning of damage to the investigation, they would not have run the story.
He said their reporter only knew "a name" and no details of the inquiry before he was briefed by the force.
Sir Cliff, who has since been questioned by officers, has strongly refuted the allegation and has not been charged. His advisers said he would not become embroiled in the BBC-police row.