The corporation has claimed that the judgement "represents a dramatic shift against press freedom" and could lead to police investigations going unreported.
A judge awarded Sir Cliff an initial Â£210,000 and he could get much more.
Sir Cliff took legal action against BBC bosses over broadcasts of a South Yorkshire Police raid on his home in Sunningdale, Berkshire, in August 2014, following a child sex assault allegation.
Mr Justice Mann said the BBC infringed the star's privacy rights in a "serious and sensationalist way".
Fran Unsworth, the corporation's director of news, said it is considering an appeal against the judgement.
A BBC spokesman said: "This judgement creates new case law and represents a dramatic shift against press freedom and the long-standing ability of journalists to report on police investigations, which in some cases has led to further complainants coming forward.
"This impacts not just the BBC, but every media organisation.
"This isn't just about reporting on individuals. It means police investigations, and searches of people's homes, could go unreported and unscrutinised.
"It will make it harder to scrutinise the conduct of the police and we fear it will undermine the wider principle of the public's right to know. It will put decision making in the hands of the police.
"We don't believe this is compatible with liberty and press freedoms, something that has been at the heart of this country for generations.
"For all of these reasons, there is a significant principle at stake. That is why the BBC is looking at an appeal."
Outside court Sir Cliff stood next to a lawyer who read a statement on his behalf.
The singer said it was "going to take a little while" as he was too emotional to talk, and added: "I hope you'll forgive me."
Lawyer Gideon Benaim said the singer never expected, after 60 years in the public eye, to have his "privacy and reputation tarnished in such a way".
He said the BBC refused to apologise and insisted it had run a public interest story.
The 77-year-old singer hugged friends after the ruling and as he left court fans clapped and sang his hit song Congratulations.
"I'm choked up," he said. "I can't believe it. It's wonderful news."