Days before he left office, Tony Blair attacked the "feral beasts" of the media who, he claimed, like to tear "people and reputations to bits". He didn't name names, other than to launch a bizarre attack on The Independent for being too opinionated. But most people would have listed The Sun and the News of the World among the papers with the sharpest teeth and the greatest appetite for human flesh.

After he stepped down, many of his political colleagues who had been victims of that bloodlust never heard from him again. Yet by his own evidence to Lord Leveson, the man who owned those titles and the woman who edited both of them became closer friends to Mr Blair than ever before.

Rupert Murdoch and Rebekah Brooks were powerful and fascinating people and stayed loyal to him as Prime Minister to the end, so maybe that explains it. But did he share more of their world-view than we thought?

Mr Blair told the inquiry he didn't change any policy to try to win favour with News International (NI). There was no deal, written or unwritten, no pact, not even an "understanding".

In many ways, Mr Blair was more a small-"c" conservative than he wanted us to believe then. So many of the stories, which so often found their way to NI journalists first, about cracking down on asylum-seekers, welfare "scroungers", drunken yobs and the like, were true to his political beliefs.

So did Mr Murdoch really have no influence on government policy? Of course he did.

Rupert Murdoch was the 24th member of the Cabinet. On many major decisions his views were taken into account. And Mr Blair explained why to the inquiry. If you own papers with a readership that runs into the millions, "that's power". That power – to influence, not to decide – was used most often on the issue of Europe.

Mr Blair wanted Britain to join the euro; Mr Murdoch did not. We didn't join. Mr Murdoch thought a referendum on further European integration was essential as a matter of principle; Mr Blair did not. But he agreed to one.

Mr Murdoch used any opportunity to speak out against the euro, and had his papers campaign to keep the pound. He didn't care what Mr Blair thought. Mr Blair spoke in favour of the euro only occasionally and very tentatively. He cared very much what Mr Murdoch thought. One man was unelected and didn't even have a vote in Britain; the other was Prime Minister with the largest majority in living memory.

That is not to say Mr Murdoch kept Britain out of the euro. Gordon Brown can fairly claim much of the credit for that. But as Tony Blair himself conceded, Mr Murdoch did have "power". Some of that power was ceded to him by Mr Blair himself. We know the former Prime Minister is a man of religious faith but his relationship to media power was like that of an agnostic to God. He wasn't sure it existed but he decided to behave as if it did just in case.

Lance Price is a former media adviser to Tony Blair and the author of 'Where Power Lies'