"We have not written directly to Sir Cliff Richard. It is the responsibility of his lawyers to ensure he is fully briefed on the conversations which have taken place with investigators.
"This is an investigation which has increased significantly in size since its inception. Sir Cliff Richard's lawyers are aware that there is more than one allegation."
He added: "In view of the expanding nature of the investigation, it would be premature and potentially misleading to predict a likely date when it will be concluded; however, we are progressing as swiftly as possible."
Two paragraphs of the letter from Mr Crompton were blacked out before being released.
In a statement released this evening by Sir Cliff, the singer stated he had no idea from where the allegations had emerged.
He said: "I have no idea where these absurd and untrue allegations come from.
"The police have not disclosed details to me. I have never, in my life, assaulted anyone and I remain confident that the truth will prevail. I have cooperated fully with the police, and will, of course, continue to do so.
"Beyond stating that the allegations are completely false, it would not be appropriate for me to say anything further until the investigation has concluded, which I hope will be very soon.
"In the meantime, I would, again, like to thank everyone for supporting me through this unbelievably difficult period."
The publication of the letter from Mr Crompton, dated February 10, followed a scathing independent report into an agreement between South Yorkshire Police and the BBC which led to a raid on the singer's home being broadcast live around the world.
The independent report found that the deal "certainly interfered with his privacy and may well have caused unnecessary distress".
Following the raid, Sir Cliff was interviewed by detectives investigating a claim of a sex crime involving a young boy, but was not arrested or charged.
Former chief constable Andy Trotter said South Yorkshire Police should never have a made a deal with the broadcaster - a decision taken after BBC reporter Dan Johnson went to the force saying he knew they were investigating the veteran entertainer.
Mr Crompton said a Metropolitan Police investigation into the source of the leak to the BBC had been unable to find the source.
A spokesman for the Crown Prosecution Service today said it was providing "investigative advice" in relation to the allegations but it had not been presented with any file for a charging decision.
The spokesman added: "The CPS is providing early investigative advice in relation to allegations of sexual offences committed by a 74-year-old man, interviewed by police in August 2014.
"The allegations remain under investigation by South Yorkshire Police."
Officers raided the home of Sir Cliff, 74, in Berkshire last August, when he was on holiday, over allegations which dated back to the 1980s and involved an underage boy.
South Yorkshire Police refused to comment on the investigation.
- Daily Mail
