The raid on the pop star’s penthouse caused controversy when the corporation broke news of the search, with a film crew reportedly arriving on the scene before the police.
In a letter to Home Affairs Select Committee chairman Keith Vaz, Mr Hall said: “I believe that BBC journalists have acted appropriately in pursuing this story. As you rightly say, the media has a right to report on matters of public interest.
“Sir Cliff Richard is one of the most successful British entertainers of all time and has been a prominent public figure for several decades. Investigations into historic sex abuse cases have — and will continue to have — a profound impact on the lives of well-known individuals and the standing of public institutions.
“The disclosure of a sex abuse allegation against Sir Cliff Richard and the police search of his property was clearly a significant story and the BBC was not alone in providing extensive coverage.”
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.
Richard, who was in Portugal when the search took place, has firmly denied any wrongdoing.
Mr Hall and the chief constable of South Yorkshire Police, David Crompton, will face a grilling by the Home Affairs Select Committee over the affair when Parliament returns from recess and the force’s police and crime commissioner has launched an independent review of what happened.
Richard’s fans have rallied round the veteran star since the allegation became public and are showing their support by buying copies of his 1992 Number Seven hit I Still Believe in You, with the song headed for this weekend’s Top 40.