A review on the cover of Christopher Hitchens’s final, posthumous book "Morality" insists that "there isn’t another Hitchens". I visited the offices of the Mail on Sunday in Kensington to meet the man who stands contrary to that dust-jacket’s praise.

I meet Peter Hitchens in the building’s foyer, and I am politely welcomed, and extended the offer of seeking a coffee shop. Hailed as the most dour and cold of conservatives, I’m alarmed by the warmth and enthusiasm with which he shakes my hand, before leading me on a tour of the nearby Kensington squares and streets. He expounds on the diplomatic area’s regal housing, winding towards a café that he assures me will be perfect for our conversation.

When we arrive, the French owner is closing up early to visit the Notting Hill carnival; but he welcomes my host with a smile, and they exchange a couple of edgy jokes about Peter’s controversial stance on immigration. We’re all grinning. The other Hitchens - the man who’s had me nervous all day - is now laughing too. Put mildly: this is not what I was expecting. We eventually bury ourselves in the corner of a different café.

Born in Malta in 1951, Peter arrived two years after his brother Christopher. Their father Eric - affectionately dubbed ‘The Commander’ - was stationed on the island towards the end of a long career of service in the British Royal Navy: with his wife Yvonne, he had moved the family abroad just after their first son’s birth. This was to be the first of many geographical shifts for the Hitchens clan as they followed the Commander between various work posts.

By the time he was fourteen, Peter was in Cambridge at the same boarding school as his brother, and from there, he would remove himself to York for university. He graduated with a Politics degree in 1973. As we’d navigated the chess board of Kensington’s pedestrian crossings, he’d laughed about his sloth as a student: time not spent relaxing was consumed with proselytizing about his growing Trotskyism. He flashes me an ironic grin when I ask about his recent 60th birthday.

"I’d probably been born to be middle-aged. I welcomed its arrival. I’m not one of those people who thought “Oh, no! I’m 40! Life has come to an end!” It’s a time of life I’d always wanted to reach, and I haven’t - so far - found it disappointing."

He also offers a lament for his teenage years:

"Being a teenager is awful. I feel great sympathy for anyone going through it. You aren’t what you want to be, you want to be what you can’t be, and you don’t understand it, and you’re not capable of understanding it until it’s over. One of the terrible things now is that you’re free to follow impulses that you really ought to restrain. That’s why being a teenager is so much worse nowadays. Nobody says “stop”."

I tense a little; here is a glimpse of the staunch conservatism that has won him such notoriety. We discuss his views on education and British society, and above all he mourns the effect of modern life on children.

"When I see - in some of the poorer suburbs of one of Britain’s larger cities - the children in the push chairs with the dummies crammed into their mouths, or children of ten with that hardened look that they can develop these days, it saddens me. People don’t know what’s good for them at that age. Adult authority is terribly important."

Sensing a shift towards the topic of lawlessness, I ask him about a recent - and cringe-making - encounter with comedian Russell Brand. Peter and he formed part of a panel about drug addiction on Newsnight. They had dueled before, and Brand had ignored Peter as a "Daily Mail bigot".

"He started again with the stuff about bigotry. I plainly listen to my opponents and take some care to figure out what it is that they think, and I offer reasoned rejections of their positions. You can call me a reactionary, you can call me anything you like: bigotry is just false. I have to defend myself against this. If you don’t respond, then it sits there. In fact, the logic of Russell Brand actually supports my position. If [heroin] does enslave you for life, then surely almost no effort should be wasted in making sure you never have that first contact."

Brand had appeared on the show to promote his BBC Three documentary on life as a drug addict, and spoke stridently - if vaguely - about the need for compassionate, non-threatening treatment of users. Peter is having none of it, and insists that preventative measures are the real solution. His new book, "The War We Never Fought" (an attack on the allegedly fictional war on drugs), was released at the start of October.

"One very effective way of [deterring users] is to make possession of this drug a very serious crime. People who haven’t got the sense to see that it’s a stupid thing to do will at least have the incentive of knowing that their life is seriously damaged if they are caught. Doublethink is incredibly common here, otherwise left wing people couldn’t sustain their belief."

Russell Brand isn’t the only leftist celebrity with whom Hitchens has brawled intellectually. At the Vanity Fair memorial for his brother, Peter’s biblical reading was praised by the comedian, writer and actor Stephen Fry. Following an almost immediate disagreement, Hitchens told Fry how little he thought of him.

"It was about him seeking me out. I was trying to avoid him."

He likens Fry to Bill Clinton: finding the one person in the room who disagrees and trying to woo them.

"I’ve never liked what I’ve seen or read of him. I didn’t want to make a scene [at the memorial]. But he seemed to be anxious to have the conversation with me. It’s dishonest to pretend friendliness to people you don’t like. We disagreed about religion, and the next thing I knew he’d put something about me on Twitter."

A tweet which was soon deleted, following criticism from Fry’s followers. It’s not hard to find online; it denounced Peter as inferior to the late Christopher, calling him a "clod".

"[Fry’s intelligence] is not what you’d call lightly worn. I don’t want him locked up, I just don’t like him. The BBC might benefit from having some other voices, and one of the things they value him for is that he uses [his Cambridge education] to espouse revolutionary views."

I feel I have him in battle mode, and ask him what gets him writing in his fiery way. Then he’s grinning again, and charming, and I’m disarmed.

"I just think it’s fun. You get your name in big print, and it has a feeling of not being left out. I’m blessed with some skill at words, so it’s easy for me. I find the idea of doing quite a lot of things - athletic, mechanical, scientific - extremely off-putting. So I want to do the thing that I find easiest."

Supping his coffee, he quotes the old Ronald Reagan joke:

"When I was a boy, I was told that hard work never killed anybody, but I didn’t want to find out if it was true or not."

It was in childhood, too, that he first developed a flair for this written word. The conversation is continually shifting - he can talk with the trademark Hitchens smoothness about almost anything. He holds court on literature, history, politics and philosophy, although he loathes any talk of theology ("I’d rather go to the dentist").

But I’m fascinated by the brothers as a pair, and I ask him if anything caused two such ardent scribblers.

"No, I think it’s easy to over-psychologize these things... [My brother] would say, with great generosity, “No, actually, if you tried to work out which one of us was going to be a journalist when we were children, it would have been Peter.” Because that was the thing I was best at."

He muses about the family newspaper he produced - "unimaginably filled with cricket scores - and assures me that, blood apart, they were always very different people.

"We got into [journalism] in such completely different ways.

The brothers both worked at the Daily Express in 1977, but apart from that:

Christopher barely worked for a daily newspaper at any time in his life. We were completely different."

Nowhere was this more apparent than in their intellectual stances. Peter responded to his brother’s best-selling atheist polemic, ‘"God Is Not Great", with his own book, "The Rage Against God. It covers their initially similar beginnings as Trotskyists and atheists, and describes Peter’s transformation to the Christian right after seeing a haunting portrayal of the Last Judgement. Despite this, the pair did have some contact: the afterword to "Rage" narrates the brothers having dinner in Christopher’s Washington apartment.

He died in December 2011, and I don’t want to press Peter too much on this recent sorrow. Alarmingly, he seems eager to continue, regaling me with heartwarming family stories, and he jokes about his brother’s seeming lack of physical grace and domestic prowess.

"There was the late night with the bottle of scotch and the unending conversation, there was the circuit of speech-making, there was the endless hours at the keyboard: but the idea of him roasting a leg of lamb, or taking a child to the playground, or mowing a lawn was just unimaginable."

Yet these are all things he confesses to having discovered about his brother, some in person, some posthumously. Despite this warm discussion:

"We didn’t have much to do with each other. He went away to school in Cambridge, and for a year nothing much happened. Then, one Christmas, he came back. And he’d left us to all intents and purposes. He wasn’t interested in being a member of our family any more, he’d found another world. He’d had the horizons of the world opened up for him, and he knew that he had to get out. He’d set his heart: it was going to be Oxford and it was going to be Balliol [College], and he was going to get out."

He’s suddenly serious.

"He was consumed with the fear of the suburb. We lost him then, and from then on he was a sort of stranger. When he was home, he was home anxious to be away. Term would come around and he was keen to be at school in the larger life that he’d got. Our father found it completely incomprehensible, our mother not much less so. He’s made this drama out of their contrasting personalities, but it wasn’t quite like that. They were both pretty baffled by him."

He pauses to gather his thoughts, and drinks more coffee.

"Because we grew up at boarding school, we didn’t have networks of friends. We were always moving anyway. We were forced on each others’ company, certainly more than he wanted. So [when he left], I felt very much deserted. He’d gone. And when people say to me that it must be terrible to lose your brother, I tell them yes, it was a pretty awful thing: but in reality, I lost him 40 years ago. We could finish each others’ sentences in private language, we knew a lot of the same things, and when we were together it was never awkward. But I wouldn’t claim any great friendliness."

Then he seems to U-turn.

"The fact that you’ve known each other longer than anybody else means that there is an irremovable closeness which nobody else can have. That served at the end quite well. It made it a lot more..."

And he breaks off, and stares past me. Consulting the recording of our conversation, he stops for over ten seconds. When he looks back at me, he isn’t crying - but his eyes aren’t dry either.

"He didn’t want to be told things, or for people to make references which suggested that he might die. I knew that. The times when I went to see him - when I knew he was dying but he wasn’t admitting it - I managed to contrive them all to be visits for other purposes. Otherwise, I felt, it would be like the bloody angel of death flapping onto your windowsill. There was always an assignment, or a speaking engagement. I never went with the specific purpose of seeing him because I felt that, if I did that, he would feel dispirited."

He gestures to the copy of Mortality on the table.

"And then I read in this that that’s exactly how he did feel."

"Mortality" is out now, available from Atlantic Books at £10.99.

"The War We Never Fought" was released on 27/09/12, available from Continuum Books at £16.99.