“This is the kind of thing he sends me,” says Robert Harris, getting up towards the end of our interview in the Fitzwilliam Hotel, to show me a video clip mailed to him earlier by none other than legendary film director Roman Polanski.

It turns out to be some hilarious footage from the Iranian coverage of this summer’s Olympics, in which the skimpy outfits during the gymnastics are covered by black bars. After we’ve both finished laughing, Harris says with a glint in his eye, “Typical Roman!”

The association between Harris – who is in town to promote his excellent new Vatican thriller Conclave – and Polanski goes back to the author’s 1992 alternative history hit Fatherland, which the director wanted to film. Although he failed to realise that ambition, he remained a keen fan of Harris’ work and was particularly taken by his ancient Roman thriller Pompeii, influenced as it was by Polanski’s 1974 neo-noir masterpiece, Chinatown.

Once more the director’s attempt to turn the book into a film were scuppered, but as Harris relays, this time there was a satisfying twist to the tale.

“Oddly enough I was here in Dublin, publicising The Ghost,” recalls the author, speaking about his 2007 novel, which was centred around a fictional prime minister who was heavily based on Harris’ long-time acquaintance, Tony Blair. “Pompeii had fallen through and I’d sent Roman a copy of The Ghost, saying, ‘Maybe we should do this instead – no volcanoes or togas.’ It was a sort of joke. But I was outside some radio station overlooking the Liffey, and the phone rang, and it was Polanski.

“I sat in the van with rain coming down, and he said, ‘You’re right – it would make a film!’ I thought, ‘Well, thanks very much, but things don’t happen like that.’ And then to my astonishment, three years later we’d made it. So it was one of those rare occasions when things happen as they’re sometimes supposed to.”

The resulting film – titled The Ghost Writer everywhere except Ireland and the UK – featured Ewan McGregor, Pierce Brosnan and Kim Cattrall amongst its cast, and proved to be a successful release that scooped several awards. Harris collaborated on the screenplay with Polanski and overall the film enhanced his reputation for creating intelligent, intricately layered stories with commercial appeal, in a manner reminiscent of John le Carre.

It’s a formula successfully repeated in Conclave, which on the day of our meeting has entered the UK book charts at number two. Inspired by the Papal enclaves of 2005 and 2013, the action focuses on the Dean of the College of Cardinals, Cardinal Lomeli, who has to negotiate his way through the shady politicking of the succession process, following the sudden death of the Pope, whose ascetic lifestyle has more than a hint of Pope Francis about it.

“I like enclosed worlds,” says Harris of the inspiration for the book. “For instance, Enigma is set in the enclosed world of the code-breakers. I like creating a cut-off community and telling the story in a tight time-frame, so this setting was perfect for me. After the 2005 conclave, a cardinal’s secret diary was published in an Italian religious magazine, and for the first time, that gave an insight into the process of electing the Pope.”

Though these days he enjoys a career as a high-flying novelist and screenwriter, Harris in fact began as a current affairs reporter, first with the BBC and then later as political editor of The Observer. It was while working as political diarist with The Sunday Times that he first encountered the aforementioned Blair, who explained to Harris the embryonic New Labour project in the aftermath of Neil Kinnock’s 1992 election loss.

Although Blair is now widely loathed on the left, there is a good chance he would be remembered as a great prime minister if he’d simply opposed the Iraq war.

“Yes, I think he’d be remembered as a great prime minister if he simply said he got it wrong,” nods Harris. “A lot of people would respect that. But to keep on insisting that the world is a better place because of the Iraq war strains people’s belief… they then lose interest. Even if that is his genuine view, he’d be well advised to keep it private.” Having known Blair for so many years, does that level of hubris surprise Harris?

“The great surprise is the person I first met in the ’90s and the man he later became,” he responds. “The Tony of ’92 up until around ’98 was a man much like us, if you like. He was a fully paid up member of the human race, quite amusing and very commonsensical actually – he was non-ideological and that was very refreshing. It was only as time went on that this rather more odd, messianic sense of being the chosen one crept in. He now seems an utterly transformed figure, although I haven’t seen him for many years.”

Turning to more up-to-date political matters, Harris’s scepticism about the Jeremy Corbyn project within Labour is well-documented (“It’s going nowhere,” he shrugs), and he’s dismayed about the outcome of the Brexit referendum.

“It’s appalling,” he says, shaking his head. “I desperately hope that it works, of course I do – I’ve got four children growing up in Britain who are about to start earning a living. I don’t want it to be a disaster, but I cannot see how emotionally, economically or in any sense it’s anything other than a leap into the dark. You only have to look at the people who are in favour of it, in my view. Anything they’re in favour of, I’m always going to be against.”

Conclave is out now, published by Penguin.