The singer successfully sued the broadcaster for filming a police raid on his home on live TV without his knowledge.
They have now agreed to pay him £210,000 in damages and contributed £850,000 to his legal fees, although the cost of the proceedings were actually £3m.
However, the corporation wanted to appeal the sum as they think the judgement could threaten press freedom in the future.
A judge refused their right to appeal the damages fee, despite barrister Gavin Millar QC, who leads the BBC legal team, calling it "wrong in law".
It could still apply directly to the Court of Appeal for permission to appeal.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
