Sir Cliff succeeded in his case against the corporation last month over coverage of a police raid on his home following a child sexual assault allegation.
The ‘Summer Holiday’ singer won close to £1m in costs and damages from the corporation and news boss Fran Unsworth was forced to issue an apology.
The police raid was part of an investigation into allegations of historic sexual abuse, for which Sir Cliff was never arrested or charged.
Despite saying sorry, Unsworth initially said the BBC would explore an appeal based on the judge’s ruling, which the broadcaster said risked limiting “the long-standing ability of journalists to report on police investigations”.
However, the corporation on Wednesday said its lawyers had found that the decision to find in favour of Sir Cliff could not be separated from the ruling on reporting live police investigations.
“Given this advice the BBC will not be appealing,” a spokesperson said in a statement. “It would inevitably mean an expensive legal cul-de-sac and one that would simply prolong Sir Cliff’s distress.
“Instead the BBC is writing today to ask the government to consider a review of the law in this important area to protect the right to properly and fairly report criminal investigations, and to name the person under investigation.
“There is a fundamental principle of press freedom at stake here and one upon which we believe Parliament, as our lawmakers, should decide.”
A spokesperson for Sir Cliff said: “Sir Cliff reluctantly took his case to court because he felt his privacy had been flagrantly invaded and disappointingly the BBC were not prepared to acknowledge that and apologise.
“He welcomes the fact the BBC have decided not to seek permission to appeal from the Court of Appeal, particularly after the judge gave his judgement that they had no grounds on which to pursue such an action.
“Sir Cliff now hopes that outstanding issues can be resolved quickly.”