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 (HASC) chairman Keith Vaz MP, 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.
Sir Cliff, 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 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.
In his letter, Mr Hall said protecting sources was "a key principle for all journalism" and "for that reason the BBC will not be providing details about the source".
He added: "I fully understand that a core part of the work of your committee is to scrutinise the work of the police, but I am sure you also appreciate that the BBC's editorial independence, as guaranteed by the BBC Charter, is something we take very seriously and is highly valued by the British public; as such it would not be appropriate to elaborate on detail of our editorial processes."
Mr Hall said a complaint by South Yorkshire Police about an article on the BBC News website would be dealt with separately by the corporation's director of news and current affairs James Harding.
Sir Cliff'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.