Mr Justice Chamberlain made the comments as he ruled against the government's attempt to have its legal costs paid by the BBC.

This followed a High Court battle over identifying an abusive MI5 agent.

The government got an injunction preventing the man being identified.

The BBC had wanted to name the man, known as X in legal proceedings, saying he abused his status as an MI5 informant to coerce a former partner.

The judge said the BBC was "entirely successful" on one issue, partly because Ms Braverman had been unable to show a leak did not come from within government.

In January, Ms Braverman - who was then the attorney general and is now home secretary - had applied for an injunction preventing X from being identified by the planned story.

Ms Braverman had initially wanted the entire case heard in private, but lost this application.

Before a hearing had taken place, the Daily Telegraph reported Ms Braverman was seeking an injunction to block a BBC story about a spy working for British intelligence.

The briefing received by the newspaper damaged the government's argument that publishing details of the case could harm national security.

Mr Justice Chamberlain today said the issue of open justice had a "special importance" in the proceedings.

He said that the BBC "was entirely successful on this issue, in part because the attorney general had been unable to negative the inference that a government source had briefed the Daily Telegraph about the case, while at the same time inviting the court to order an entirely private hearing".

A government leak inquiry was ordered into who briefed confidential details to the newspaper.

Ms Braverman was one of those investigated by the leak inquiry, the BBC understands.

The government has not responded to the BBC's questions about the inquiry, including as to whether Ms Braverman was questioned.

Last month, No 10 defended her after questions about her relationship with MI5 because of the leak.

Prime Minister Rishi Sunak reappointed Ms Braverman as home secretary days after she quit for breaching the ministerial code by sending confidential material via a private email account.

Because an injunction was granted, after the judge said identifying X would create a risk to him, the government argued its legal costs should be paid by the BBC.

The judge dismissed that claim on Friday, saying the BBC had been able to publish a detailed story "far beyond" the initial broad restrictions sought by the government.

"Applying common sense", he ruled, "the outcome was mid-way between what the attorney general had initially said she would accept and what the BBC wanted to publish."

Both sides will pay their own costs, which is what the BBC had argued for.

The BBC investigation included interviews with two former partners of X, one of whom had filmed the MI5 agent attacking her with a machete.