Tony Blair has said that he “toyed with Marxism” as a young man after being inspired by a biography of Leon Trotsky that detailed “extraordinary causes and injustices”.

The former prime minister, who rebranded his party “New Labour” in the belief it would be most electable as a centre-ground party, said yes when asked in a BBC interview if he was “briefly a Trot”.

The politician – who faced repeated rebellion from leftwing Labour MPs, including Jeremy Corbyn, who believed Blairism had dragged the party to the right – said the first volume of Isaac Deutscher’s trilogy “opened a different world” for him and changed his life.

“Here’s this guy Trotsky who was so inspired by all of this that he went out to create a Russian revolution and changed the world. I think it’s a very odd thing – just literally it was like a light going on,” Blair told Reflections with Peter Hennessy on Radio 4.

“And even though, you know, over time I left that side of politics behind, the notion of having a cause and a purpose and one bigger than yourself or your own ambition – and I think probably allied at the same time to coming to religious faith – that changed my life in that period.”

Blair said the period was “reasonably brief … it wasn’t longer than a year probably” – describing a later influential conversation with an Indian graduate student who argued that the “state too can become a vested interest”.

Blair described Cherie Booth, who was to become his wife, as a mainstream Labour supporter who had “complete contempt for the far left, which was an unusual position for young people” and who was critical of his “sort of Oxford student socialism”.

In remarks that carry an ironic resonance for the former leader’s reputation among Corbyn-supporting Labour members today, Blair also claimed that the party was regarded as a “kind of anathema” for socialists when he was a student. “These were the betrayers of socialism, these were the people who, you know, didn’t really believe in the way you should believe,” he said, arguing that he was critical of the leadership of Harold Wilson and Jim Callaghan when he first joined the party for that reason.

He said Cherie never changed her politics and put it down to growing up in a working class part of Liverpool and realising “you actually needed people to govern and govern sensibly to improve people’s lives. And yet she would rather have given up the ghost than vote Tory”.

Blair’s comments come as Corbyn begins a national tour of marginal constituencies after his more leftwing brand of politics surprised critics by stripping Theresa May of a majority in June’s general election.

In a long interview about his life and career, Blair also talked about his relationship with Gordon Brown, saying the pair had once been “so close” that they had spoken several times a day.

He said the Granita pact – in which they were said to agree that Brown would step aside for Blair as candidate for leader, but that Blair would step down after two terms to make way for his colleague – did not happen at the Islington restaurant it is named after.

“Well, the truth is it wasn’t in Granita restaurant. We did have dinner in the Granita but we’d already decided what we were going to do. The actual conversation, I think, took place in a couple of different places in Edinburgh,” he said, adding that they were in two different old schoolfriends’ houses.

He said Brown had taught him an “immense amount”, including how to make a speech, starting by helping to rewrite his first conference speech that got an “extraordinary reaction”.

Explaining his decision to court even rightwing media barons, Blair described watching the “viciousness of attacks” on Neil Kinnock, which he “probably became too affected by, to be blunt”.

“Because at that point, you know, the media was immensely powerful in its ability to shift opinion and it was so negative on him that it really didn’t matter whether what he said was sensible or not sensible,” he said.

Blair argued that his team was simply determined not to be “kicked around in the way that, frankly, Neil and his team had been”.

The former Labour leader also turned to his greatest controversy in power: the decision to take Britain into war with Iraq alongside the US. He claimed that he had “Chilcoted” himself several times, meaning subjecting himself to the same scrutiny as the Iraq inquiry chair, Sir John Chilcot, did.

He said he accepted there were mistakes over Iraq, including the faulty intelligence and the exit plan, but added: “The thing that is, I think, difficult for people to accept is that I haven’t changed my view that it was better that we removed him [Saddam Hussein] than not,” he said.

And Blair defended his close relationship with George W Bush, which seriously damaged his reputation with many British voters, by saying that he was clear that after the 9/11 terror attack the UK “bonded with America in a deep way”.

“I took a decision after 9/11 that we should be shoulder to shoulder with America in dealing with this. I thought it absolutely essential. I still think this alliance with America is fundamentally important to our security,” he said.

However, he conceded a failure to understand the “depth of the problem” that would be unleashed in the aftermath of the conflict.