Richards’s apartment was searched by officers from South Yorkshire and Thames Valley police last week as part of an investigation into the alleged sexual assault on a boy at a religious event in 1985.
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 performer, who was in Portugal when the search took place, has firmly denied any wrongdoing.
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 on the Home Affairs Select Committee over the affair, and the force’s police and crime commissioner has launched an independent review of what happened.