“Afternoon, Chris,” shouts a smiling stranger.

“Afternoon,” Chris Tarrant calls back, as he stands by Marylebone station in London, having his photo taken.

“This is very civilised!” the elder statesman of light entertainment says. “I’m so much part of the furniture now. It’s just: ‘Hello, Chris. All right, mate.’ The classic still is ‘phone a friend’. I had three this morning. ‘All right, Chris, phone a friend! Phone a friend!, PHONE A FRIEND!’,” he says in a variety of cartoon voices.

Well, after presenting 600-odd episodes of Who Wants to Be a Millionaire?, he can’t expect anything different. “It doesn’t bother me,” he insists.

If he wasn’t Chris Tarrant and he came across him in the street, would he greet him with that catchphrase? “I’d like to think I wouldn’t, because it’s pretty crass. It’s happened every day for 20 years now.”

We retreat to a nearby hotel for coffee. Tarrant used to be omnipresent on TV and radio. But these days he is semi-retired, following a stroke on a plane four years ago. He has continued travelling the world making documentaries, though, and now he is back with a most un-Tarrant-like project about the railways of the Holocaust. Despite the trademark chirpy voice, it makes for sombre, painful viewing.

“Without the railways, the Holocaust wouldn’t have happened. I don’t actually think the second world war would have happened without them,” he says.

The programme shows how the trains took Germans to Hitler’s mass rallies in the early days of his rule. As he pursued his Final Solution, there is the sickening sight of Jews being herded into cattle trucks and sent to death camps.

Tarrant in 2000 on Who Wants to Be a Millionaire? Photograph: Andy Hall/The Observer

The testimonies from two Jewish survivors are particularly gruelling. There is Arek Hersh, who was sent to Auschwitz at 11 and survived only because he claimed he was 17; he was sent into the line for slave labour rather than the gas chambers. He ate grass and the leather from his shoe to stop himself from starving. Then there is Helga Weiss, who at the age of 12 was transported to Terezín, where she saw seven boys forced to dig their own graves and then hanged for the crime of writing to their parents.

Tarrant says he has had nightmares since making the documentary. “They are almost entirely about the gas chambers. The claustrophobia and the horror and the screams. The scratches on the wall were 8ft high. I asked how could they scratch so high, and I was told because they would be climbing over dead or dying people trying desperately to get some air.” He comes to a stop. “Can you imagine the screaming? When I came out, I thought I was going to throw up.”

Does he normally have nightmares? “No, hardly ever.” He is not generally given to fear, or doubt. At 72, he is still a brute of a man – 6ft 2in, broad shouldered, huge hands, legs like sequoias.

Tarrant is obsessed with war and railways. The obsession goes back to his father, Basil, who died in 2005. Tarrant has often said his father, a working-class boy who became an army major, then a successful businessman, was his best friend; they drank and played together and talked about everything – except his war experiences. Those were taboo. For a long time, his family didn’t even know he had fought at Dunkirk. In 2014, Tarrant wrote a book about his father’s war experience. “Occasionally, Dad would say: ‘Those poor sods at Dunkirk.’ It turns out he was one of those poor sods at Dunkirk and he was one of the last ones off the beach.” This documentary is another way of making sense of his father’s life.

Tarrant says he is a changed man since his stroke. I assume he is talking about the kind of work he wants to do, but he is actually talking about booze. “I don’t drink whisky at all now. Nobody told me not to,” he says proudly. How much did he used to drink? “A lot. I liked it. Neat.” Could he get through a bottle in a day? “Not in an evening, no!” He looks appalled. A half bottle? Now he looks insulted. “I’d get through a half watching telly, oh God, yes. I was never crawling on the floor or drinking out of dustbins. I was never an alcoholic.”

Tiswas with (from left) Chris Tarrant, Sally James, Bob Carolgees and John Gorman. Photograph: ITV/Rex/Shutterstock

Tarrant looks at me, disapprovingly. “God. You look terribly anxious,” he says, out of the blue. He orders me to relax. It sounds familiar, but I can’t think why. Then I remember that it is what he often used to say to Millionaire contestants.

He admits there were times he feared he was an alcoholic. So he checked himself out at the doctor’s. “At the end of the tests, they said you are not an alcoholic, but you’re a heavy drinker. Carry on like this and you may become one.”

Not that he has stopped drinking. In January, he pleaded guilty to drink-driving and received a 12-month ban. Daft of him, he says – and mean of the bloke in the pub who reported him to the police as he drove off. “Stitched up, I was.” Did he know the man? “Nope. Complete stranger.” Why did he do it? “Because I’m me. If it had been you or any of my mates down the pub, he wouldn’t have bothered. I’d probably only had one more than I should have.”

Anyway, he says, the ban comes to an end at midnight on Thursday and he can’t wait. What is the first thing he is going to do? “Go for a drive. Assuming I’ve not had a drink. Which I won’t. I’m not an idiot. I’ll get in my car at midnight and drive round the block for half an hour or so.” He smiles. “I bet you I get pulled up.”

Has anything good come out of the ban? “Well, Jane has been driving around Berkshire in my Bentley. I don’t know if that’s good or bad.” Jane Bird is his partner of 12 years. Tarrant has been divorced twice and has six children (four biological, two he brought up as his own from his second wife Ingrid’s first marriage). His split with Ingrid was tabloid gold. “There has been a whole rainforest written about it,” he says. It is true – from his ex-wife’s suspicions, to her hiring a detective, discovering he had been having a long-term affair, and allegations of meanness, jumping into bed “reeking of carp, bream and pike”, and a need for Viagra. Some of his children fell out with him for a while, but he insists they all get on brilliantly with him now. He reminds me that he said nothing in response to the allegations, except to apologise for the hurt he had caused. “You won’t find a quote from me and you won’t get one today.” He says his children are too important for him to go down the score-settling route.

There is a refreshing directness to Tarrant. If he is offended, he can’t help but show it – and then some. He often says that what you see is what you get with him. But it is slightly more complicated because there have always been two distinct Tarrant personas – fun-fuelled, blokey Chrissy Wissy on the radio and the more restrained, teacherly Tarrant on Millionaire. Today, I see both – one minute he is the warm, relaxed Tarrant, the next he is pulling me up on my lack of professionalism.

When I ask about the difference between the private and public Tarrant, he gives me my first major ticking-off. “You keep jumping. There’s no train of thought to your questions,” he says grumpily.

Am I being a really bad interviewer?

“You’re not great,” he says. I apologise. “But you’re a very nice man, actually,” he adds, slapping my leg a little harder than I’d like.

How does he feel about the state of the world? “Oh, that old question!” Actually, he says, he is astonished to find himself looking back on the cold war with relative affection. “Interestingly, George Bush now seems like an enlightened individual. Trump is extraordinary; an idiot.”

As for Brexit, he has done a U-turn. “I voted to remain, and two years on I’m now a staunch Brexiteer.” Why? “I’m so utterly sickened by the European elite creaming it off on a Blatter scale. I think the sooner we get out, the better. We will survive and carry on very nicely because we’re British. I’ve been appalled by the way they’ve treated us. All this stuff about: we’re going to teach you a lesson.”

After making a programme about the second world war, does he not worry about a rise in British nationalism? “No, I’m very patriotic. I’m very British and I’m very pro-British, but that in no way means you therefore exterminate anybody else you meet who doesn’t come from Britain!”

Is migration an issue? He nods. “There’s a point at which we have to control our borders. The bottom line is the world is full up and the population on the planet is getting bigger and bigger and there ain’t much room any more. So, how’s it going to work? I don’t know.” It’s a rare moment of uncertainty.

Tarrant has never lacked confidence. He grew up in Berkshire, boarded at the prestigious private King’s School in Worcester and studied English at the University of Birmingham – a confident boy who became a confident man. He once allegedly boasted of drinking 20 pints, smoking 60 cigarettes and sleeping with four women in a single day. After working as a hod-carrier, a truck driver, an English teacher and a researcher at the Central Office of Information, he witnessed a TV news reporter in action and thought: that’s the life for me. “He got out of a very nice, expensive car, interviewed a man with a few Hereford cows, did a sign-off, then got into his car and drove off home, and I thought, bloody hell, that’s not a bad old gig, that looks like a piece of piss, I could do that. And, actually, it’s been like that ever since. Wogan said: ‘I’ve never done a day’s work since I left the bank.’ And I think that – it’s not very hard, what I do.”

He famously wrote to TV stations announcing: “I am the face of the 70s and this is your last chance to snap me up.” He got a job as a reporter on ATV, specialised in items about men with ferrets down their trousers, was offered a job in 1974 hosting Tiswas, the new ITV Saturday morning show, and never looked back. Tiswas couldn’t have been more different from the stuffy jumpers on the BBC. It was anarchic (guests being pied by the Phantom Flan Flinger), surreal (the brilliantly shambolic ventriloquist act Bob Carolgees and Spit, a dog that spat as it barked), funny (young Lenny Henry impersonating newscaster Trevor McDonald), sexy (Sally James presenting along with Tarrant, who was then a flaxen-haired, oafish pretty boy) and weirdly educational. Tarrant adored the show. “God, rolling about in custard with Annie Lennox and Sheena Easton and being paid. What a gig!”

He suddenly looks at his watch. “Good God, is that the time? I’ve got to go.”

But we’re in the middle of the interview, I say.

“It better be a helluva piece of art, this bloody thing,” he huffs.

Which job has given him most pleasure? Easy he says – radio. For 17 years, he presented Capital’s breakfast show, and made a huge success of it. It was classic Tarrant – funny, upbeat, rocktastic and laddish. He delighted in insulting his sidekick Kara Noble, telling her she had a face like King Kong’s backside and that if she had one more brain cell she would qualify as pond life.

It is more than 30 years since he started at Capital – and feels even longer culturally. This was an age when wild and wacky DJs could get away with all sorts in the name of fun. Does it upset Tarrant that, post-Jimmy Savile, this era has been reassessed and the reputation of many pop DJs has suffered? For a second, Tarrant goes silent. Then he explodes. “God! GOD! YOU CAN’T SAY THAT. No, hang on. You can’t say ‘the reputation of radio DJs’ because one of them was the most disgusting pervert in the history of the world. Most of the other guys who work on radio are very nice men who don’t go round fiddling with two-year-old children in bloody mental homes. You can’t say that!”

I can understand why he responds with such anger, but he won’t let me get a word in. “No, no, hang on, it was an era when things were different. Yes, things have changed. Yes, God, blokes were less careful in those days with how they behaved towards women. But … nobody can convey the disgustingness of Savile or Weinstein or any of these people. There’s a difference between touching a girl on the left buttock in 1971 to full-scale rape or whatever. It’s disgusting.”

Tarrant in 1989 with Kara Noble on Capital’s breakfast show, which he presented for 17 years.

Photograph: Chat/Rex/Shutterstock

What could you get away with then that you couldn’t now? “I think we were just less respectful of women, full stop. We were. The world has changed very fast. I would never condone the behaviour of Weinstein, Cosby …”

In 1999, three weeks before the wedding of Prince Edward and Sophie Rhys-Jones, the Sun splashed with an 11-year-old photograph of the future princess topless. It showed Tarrant, wearing shades, in the back of a car next to the exposed Rhys-Jones, alongside the headline: “Sophie just laughed as Chris pulled up her bikini.” It caused an outcry. The Sun was forced to apologise, Noble - who had flogged the picture for a rumoured £100,000 - was sacked from Capital, and Rhys-Jones, who had been a junior publicist at Capital in her early 20s when the picture was taken, was treated with enormous sympathy. Interestingly, at the time, so was Tarrant.

Both are laughing in the picture. But, looking at it now, you can’t help thinking Tarrant, then a star DJ in his 40s, would not be treated so sympathetically today. Surely this is an example of something he couldn’t get away with now? He says it was just a fun trip to the beach. “Basically, it was a girl in the back of a car with a load of us, all laughing. She was sort of fully clothed, but in swimming clothes I think. There was no taking off her bra or anything like that, and it was an 11-year-old photograph. The insinuation was that Sophie and I had an affair, which was totally not true. It was just outrageous.”

But wasn’t it equally outrageous that you were pulling down her top? “She wasn’t topless!’” he says belligerently. It’s as if the more he says it, the truer it will be. “You want to see the photos. She. Was. Not. Topless.”

It is astonishing if he can’t remember the pictures because the incident caused such a stink. I saw the pictures today, I say. But I’m not sure he has heard. He is still seething at the idea they had a relationship. “It was a disgruntled ex-employee trying to make money. And there was no basis in it at all. We never had an affair. We were just old mates. Nothing ever happened.”

The room feels horribly tense. I change the subject and ask what made Millionaire, which he partly devised, such a brilliant show. He relaxes and talks about the simplicity, the drama, the silences, the closeups. “You have big, wide shots normally in game shows, but here you see into their bloody soul. Paul Smith, the boss man, said this is the best soap on British television, and it kind of was.”

He says the show is making a comeback in the UK – but with Jeremy Clarkson rather than Tarrant in the driving seat. “I’ve done it, I’ve loved it. I don’t want to go back. I don’t want to go back to Capital Radio. I don’t want to go back to rolling in custard with Sheena Easton and Annie Lennox.” He stops and grins. “Actually, I probably do.”

He stands up to leave, then sits down again. There is something on his mind. “For God’s sake!” he says. “I’m not happy about the Savile stuff. Come on man, that’s horrible that stuff.”

What he says next is virtually stream of consciousness. “This Kavanaugh thing. He drank lots of beer when he was 18! All 18-year-olds drink beer. There’s a very clear line, and Savile and Weinstein …” He talks about how Savile would walk up to Sally James back in the day, lick her arm and ask when they were going out for dinner. “She hated it,” he says. And he talks some more about how shocked he was when Rolf Harris was jailed for sex offences. “We were like Harris? Rolf Harris?! He used to play the half-time entertainment at an annual charity cricket match. God!”

He gets up decisively. It was nice to meet you, I say. “Yeah, good fun,” he says. But I’m not sure he means it.

On his way out, he turns round one last time. “Make it a nice family piece or I’ll come round and break your legs.” He’s smiling, I think.

• Hitler’s Holocaust Railways with Chris Tarrant airs on Sunday 28 October at 9pm on Channel 5.