No arrests have been made and Cliff Richard, 73, who is abroad, said the allegation was “completely false”.
Police said the allegation involved a boy under 16.
The alleged assault happened at a 1985 event where preacher Billy Graham appeared at Bramall Lane, Sheffield.
The allegation is believed to have been reported to police recently.
The search in Sunningdale was carried out by South Yorkshire Police.
The investigation is not connected to Operation Yewtree and police said officers from that operation – set up by the Metropolitan Police to investigate hundreds of allegations in the wake of the Jimmy Savile scandal – had been notified.
Thames Valley Police said it had assisted the South Yorkshire force with the execution of a search warrant at the property.
Eight plain-clothed police officers in five unmarked cars arrived to conduct the search.
Cliff Richard has responded to the police search of his apartment in a statement, which said: “For many months I have been aware of allegations against me of historic impropriety which have been circulating online.
“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. Beyond stating that today’s allegation is completely false it would not be appropriate to say anything further until the police investigation has concluded.”
Cliff Richard’s spokesman said the singer would not be conducting interviews at this time.
The singer left his home there on Thursday morning and has travelled with his sister to another part of Portugal for a few days.
Cliff Richard, born Harry Webb, is one of the most successful British musicians of all time.
Sir Cliff Richard was knighted in 1995 and performed at the Queen’s Diamond Jubilee concert at Buckingham Palace in 2012.
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