Fans of the veteran pop star have been showing their support by buying copies of his 1992 Number 7 hit I Still Believe in You and it is less than 500 copies off the Top 40.
Midweek sales figures released by the Official Charts Company put the track at number 43 today.
Sir Cliff announced yesterday that he was pulling out of a charity event at Canterbury Cathedral on September 26, with his spokesman saying the star “doesn’t want the event to be overshadowed by the false allegation and has therefore withdrawn”.
The singer’s apartment was searched by officers from South Yorkshire and Thames Valley police last week as part of an investigation into an alleged sexual assault on a young boy at a religious event in 1985.
Sir Cliff, who was in Portugal when the search took place, has firmly denied any wrongdoing.
Fellow showbiz veteran Cilla Black has rallied to his defence saying she thinks allegations that he sexually assaulted a boy in the 1980s are “without foundation”.
In a statement, Cilla said: “Cliff is a very close friend of mine and has been for a million years.
“I, like everyone else, was shocked to hear of these allegations and I am absolutely positive that they are without foundation.”
The raid on the pop star’s Berkshire penthouse caused controversy when the BBC broke news of the search, with a film crew reportedly arriving on the scene before the police.
The corporation’s director-general Tony Hall and chief constable of South Yorkshire Police David Crompton will face a grilling by MPs over the affair, and the force’s police and crime commissioner has launched an independent review of what happened.
Mr Crompton and Lord Hall have been warned to stand ready to give evidence to the Home Affairs Select Committee (HASC) after Parliament returns from recess.
Committee chairman Keith Vaz has written to both men asking a series of questions about how the BBC found out about the planned search, and asked them to reply by midday on Friday.