The racehorse trainer also accused police of treating them "like terrorists" when their home was raided and even their daughter's cot was searched for evidence.
Mrs Brooks initially kept hold of her job as a News International chief executive despite twice offering to resign as the hacking claims intensified. But Mr Cameron heaped pressure on the former tabloid editor by telling MPs at the time that he would have accepted her resignation.
The Prime Minister has known Mr Brooks since their days at Eton. In 2009, he attended the couple's wedding and regularly socialised with them as part of the so-called Chipping Norton set.
In an interview carried out in December 2012 but broadcast for the first time, Mr Brooks said: "I was a little bit disappointed when he commented in Parliament on whether Rebekah should resign or not because I didn't really feel he had all of the facts at his fingertips."