The 73-year-old, who is currently out of the country, said in a statement, "For many months now I have been aware of allegations against me of historic impropriety which have been circulating online.
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Sir Cliff Richard's home in Berkshire has been searched by police
"The allegations are completely false. Up until now I have chosen not to dignify the false allegations with a response, as it would just give them more oxygen.
"However, the police attended my apartment in Berkshire today without notice, except it would appear to the press.
"I am not presently in the UK but it goes without saying that I will cooperate fully should the police wish to speak to me.
Cliff Richard issued a statement saying the allegations against him are 'completely false'
"Beyond stating that today's allegation is completely false, it would not be appropriate to say anything further until the police investigation has concluded."
The search of the property in Sunningdale was undertaken on Thursday by eight plain-clothed police officers.
A spokesperson said that the allegation against Cliff – born Harry Webb - dated back to the 1980s in the South Yorkshire area. It has been confirmed that the investigation is not connected to Operation Yewtree, although police said officers from that investigation have been notified.