Sir Cliff, 73, born Harry Rodger Webb during the British Raj in Lucknow on October 14, 1940, is one of the most successful English musicians of all time.
A number of items have reportedly been removed from the property in the Sunningdale area ofBerkshirefor further investigation, but no arrests have been made.
A police spokesperson said the allegation involved a boy under 16 at the time and dated back to the 1980s in the South Yorkshire area.
In a statement, Sir Cliff denied the allegations and 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 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."
He added: "I am not presently in the UK but it goes without saying that I will co-operate 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."
The search is not connected to Operation Yewtree, which is looking into historical claims of sexual offences by prominent media figures.
However, officers from the operation have been notified, according to a BBC report.
The actor-performer has sold 21.5 million singles - more than any other male British artist - and is the only performer to have had at least one UK top five album in each of the last seven decades.
Considered a life-long bachelor, Sir Cliff has represented the UK in the Eurovision song contest twice and in 2013 released the 100th album of his career.
He was knighted in 1995 and performed at the Queen's Diamond Jubilee concert at Buckingham Palace in 2012.
Sir Cliff shot to fame in the 1950s with his group The Shadows and his big worldwide hits include songs like 'Congratulations' and 'Summer Holiday.'
His father was a contractor in the Indian Railways and the singer was raised in a modest home in Hazratganj in his early years. The family returned to England in 1948 after India's independence.
As well as homes in Berkshire and Portugal, Sir Cliff also has a 6-million pound property in Barbados.