Mr Straw said he “made arrangements” with the then editor of The Sun to commute into London together from Oxfordshire, where they both had homes: “During my period as justice secretary, I would often travel to London on a Monday morning from the West Oxfordshire station of Charlbury.
“Mrs Rebekah Brooks used to use the same train.
“After a while we made arrangements to meet up and sit together for the journey... We would talk about what was in the papers. We’d gossip about personalities, and that sort of thing. We weren’t nattering the whole journey.”
He stressed the conversations were not too sensitive because there were always people “earwigging”.
The encounters petered out after Mrs Brooks became News International chief executive in 2009.
Mr Straw said Labour’s links with journalists had become “very, very close, sometimes incestuous” in opposition, and that continued after 1997.
Asked about Murdoch’s influence, Straw said the owner of The Sun and The Times had “power”.
“He reckoned his political influence would be greater if, as it were, his support was available in return for what he thought he could get out of it,” he said.
“I don’t mean a deal, because I have seen no evidence of a deal. But he thought there was something in it.”