Veteran Conservative and former Chancellor Ken Clarke has said David Cameron may have "done some sort of a deal" with Rupert Murdoch in advance of the 2010 election, when Mr Murdoch's newspapers switched their support back to the Conservatives.

Mr Clarke was giving evidence to the Competition and Markets Authority, and their inquiry over Mr Murdoch's attempted Sky takeover, and suggested former News of the World editor Andy Coulson had been installed as "Murdoch's man" in 10 Downing Street.

Mr Cameron made MR Clarke Justice Secretary after winning the 2010 election, and Mr Clarke recalled an incident in which he had been asked to have a meeting with Rebekah Brooks, the Chief Executive of what was then called News International. He said she told him she was now "running the Government" in partnership with Mr Cameron, a conversation he says he "took not the slightest notice" of.

The former minister, who served as Mr Cameron's justice secretary from 2010 to 2012, told the CMA: "Quite how David Cameron got The Sun out of the hands of Gordon Brown I shall never know. Rupert would never let Tony (Blair) down because Tony had backed the Iraq war.

"Maybe it was some sort of a deal. David would not tell me what it was. Suddenly we got the Murdoch empire on our side."

Mr Clarke said: "Within a week or two we had got Andy Coulson on board - I think he was Murdoch's man, that was part of the deal I assume - as the press officer. I am not being totally indiscreet. Nobody seemed bothered by it very much.

"Within a few weeks of taking over, my Prime Minister arranged a meeting with Rebekah Brooks. Rebekah Brooks described herself as running the government - now in partnership with David Cameron.

"I found myself having an extraordinary meeting with Rebekah who was instructing me on criminal justice policy from now on, as I think she had instructed my predecessor, so far as I could see, judging from the numbers of people we had in prison and the growth of rather exotic sentences.

"She wanted me to buy prison ships because she did accept that the capacity of the prisons was getting rather strained... She really was solemnly telling me that we had got to have prison ships because she had got some more campaigns coming, which is one of her specialities.

"I regarded this as a very amusing conversation and took not the slightest notice. As long as I was Justice Secretary we would not have any of this. I do not think my successor (Chris Grayling) needed any promoting from Rebekah so it all went back to the norm."

Mr Clarke said he did not know how often Mr Murdoch now visited Downing Street, but suggested he believed Prime Minister Theresa May would still be in contact with influential media proprietors.

"This rumbles on through politics. It still does," he said.

"I do not know how often Mr Murdoch goes in to Downing Street. He does not come to England as often he used to, pretty regularly before, I think.

"The Prime Minister, and Ms May's advisors, would tell her that she cannot possibly stop seeing those people.