Giving evidence for a second day, Evans explained that he had been "monstered" by a senior colleague and told his job was on the line if he did not come up with an exclusive.
Evans said: "That weekend I did everything I could to make sure I came back with a front-page story. I hacked every phone I could possibly think of hacking, that included one of an actor called Daniel Craig."
He added: "On that voicemail, I heard a female voice saying, 'Hi, it's me. I can't speak. I am at the Groucho with Jude, I love you'."
Evans said when he checked the number of the person who had left the message, it matched that of Miller, who was a regular fixture in tabloid newspapers at the time. He said he had gone to work after the weekend with his "tail wagging" and had played a recording of the message to Coulson and other journalists at the paper.
He told jurors: "Andy became very animated, [saying] 'brilliant'." Another senior colleague had told him: "You're a company man now, Dan."
Evans said after listening to the voicemail recording, Coulson ordered that a copy be made and the original destroyed.
He went on: "Andy wanted to preserve the tape but not in its original recording so he said to me, 'You need to make a copy of the tape. Put it in a Jiffy bag and have it sent down to the front gate and get them to say it has been dropped in anonymously'.
"The idea was that if push came to shove we would say that someone had sent it in and that's what sparked it all off."
The day before, the Old Bailey heard how one of Law's relatives had also sold information to the newspaper about the relationship, but the intercepted voicemail helped to confirm the story.
Evans also told the court he would like to apologise to all of the people whose privacy he had infringed.