I had that Tony Blair in the car yesterday. Had to turf him out in the end, though, or I would have been late for work.

The former prime minister talked about many things, perhaps most surprisingly that he was “briefly a Trot” – and not just on a wet Tuesday afternoon but for a whole year.

Blair was on the radio rather than in the car with me, although I’d be willing to offer him a lift to the vaguely picturesque middle of nowhere that is Howden, should he wish to go there. He was talking to the historian Peter Hennessy in an hour-long interview, first in a new series on BBC Radio Four, called Reflections. And it was a good listen.

It is common to dislike Blair nowadays, with those on his own side displaying the strongest aversion. Hating Blair and all he stands for is almost an article of faith among arch Corbynites, who see “Blairite” as the ultimate insult.

There are various reasons for the antipathy, partly that Blair was around for ages and travelled in that time from shiny idealist to a man harried by his decision to take Britain into the war against Iraq.

Those who disparage Blair believe that he took Labour too far to the right – a theory supported by the fact that he was much admired by David Cameron. Chief among those critics at the time was Jeremy Corbyn, who now leads the party and is tugging it back towards the left. Pulling a rug with furniture on is hard work, and there is a Blair-shaped sideboard on that rug, however much Corbyn might wish it had been sold off years ago.

As someone who liked Blair and then slowly went off him, I think the determination to scrub him out of Labour party history is a mistake and a shame. He was a successful leader and, for a while, a popular one. And his achievements include helping to foster peace in Northern Ireland – a process started by John Major – alongside introducing the minimum wage, devolution and repairing the NHS, left in a parlous state by long Tory years.

The NHS was repaired and restored, although, sadly, by introducing dodgy private finance deals, a Tory idea that Labour embraced with reckless enthusiasm.

Anyway, history will have the last word – and history may be kinder to Tony Blair than people now are. And whatever picture emerges, Hennessy’s programme provides much to argue about.

The intimacy of radio works so well for this sort of interview, and Blair was mostly straight and upfront, with occasional convenient lapses of memory, or careful verbal swerves. And the “you knows” are still there.

History is often shot through with irony, and it was striking to hear Blair say that the Labour Party of the 1970s was “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, adding that he was critical of Harold Wilson and Jim Callaghan when he joined the party.

Travel from student days in Oxford to the thin oxygen of the post-political life, when he is a ghost wandering the corridors of time, and Blair is now anathema to the sort of old-school socialism Jeremy Corbyn flourishes with a surprising degree of success, for now at least.

Footnote: Madame Tussauds is said to be preparing a new waxwork of Theresa May. There’s optimism for you. The wax version of our waxy prime minister won’t be ready for months. Perhaps Tussauds knows something we don’t.