The Alfie star appeared in wood-panelled Court 12 of the Old Bailey, giving evidence in the phone hacking trial.
Former government spin doctor Andy Coulson, who was editor of the News of the World (NotW) from 2003 to 2007, is accused of conspiring to hack phones between 3 October, 2000 and 9 August, 2006, along with ex-News International chief executive Rebekah Brooks, 45, and former NotW managing editor Stuart Kuttner, 73.
The actor was quizzed by then-NotW editor Coulson’s lawyer, Timothy Langdale QC, about a story about his then- girlfriend Sienna Miller having an affair with actor Daniel Craig.
The lawyer wrote down a name of a source on a piece of paper to show the witness. The name was not read in court.
Law told the jury that he had discovered last autumn that the relative had passed on information, but had never heard claims they had been paid.
He said: “I was made aware very recently that there had been some kind of communication with this person and several others in and around and about this period of time. I was never aware any money had been exchanged.”
He told the court he first became aware of rumours of the affair around the time the couple went to Ms Miller’s sister Savannah’s wedding in the West Country and Law was shown NotW articles headlined “Sien-na Cheats On Jude” and “Layer Fake”. There was a ripple of laughter when asked to read an article, Law replied: “I would rather not.”
The jury heard that he had telephoned Craig to confront him about the affair and suggested he should tell his own girlfriend, Satsuki Mitchell, about it.
But he could not remember whether that was before or after the paper broke the story and he had not left a voicemail about it.
Asked if he was aware that anyone around him was leaking stories, he said: “No, I did not know that anyone around me was talking to the newspapers, although I suspected it because there was such a flow of information … I suspected many people over that period of time.”
He was also shown the names of a friend who is a publicist and an employee who it is claimed passed information to the press.
Miss Miller first alerted him to the claims about the employee in 2011 or 2012, Law said.
Earlier, he described to the jury that the media had “an unhealthy amount of information” about his life and that packs of photographers would follow him around even when he made secret arrangements.
The 41-year-old Cold Mountain star described how press attention began to intensify when he was nominated for an Oscar for The Talented Mr Ripley in 2001. It grew throughout his divorce from Sadie Frost and then during his relationship with Miss Miller, he told the court. Law said: “There seemed to be an unhealthy amount of information that people, or someone, had that meant they had access to my life and my whereabouts, what I was doing and who I was with.”
He said when police showed him notes that private investigator Glenn Mulcaire held about him, he “was shocked to see the amount of information that had been accumulated”, but he added: “Sadly it didn’t surprise me because it seemed apparent from what had been written [in the press].”
He told the jury that from around 2001 photographers would gather at his home.
“Around 2001 and over the following four or five years the daily appearance of packs of photographers either on the street or in cars became a very regular occurrence.”
He added: “I became aware that I was also turning up at places having arranged to go there secretly … and the media were already there, or photographers were already there.”
The press interest even followed him to the United States, where he worked filming Cold Mountain and Alfie in 2003, the court heard.
All seven defendants in the case deny the charges against them.
The trial continues.