Doing an interview over the phone can be a thankless job: lines get crossed, you awkwardly interrupt one another and, without the intimacy of a face to face encounter, it’s hard to get a sense of the other person. But doing a phone interview with Brian Cox – the acclaimed actor, that is, not the pop-star-turned-particle-physicist with the same name – is such a hoot that if we met in person I would have probably dissolved into a puddle of hysteria.

“No, no, not now, I’m having an important conversation!” he barks when someone has the temerity to try to enter his hotel room 45 minutes into our chat. “So where was I? Ah yes …” And he launches back into the anecdote about the time Princess Margaret felt him up. The man has so much charisma – and so many anecdotes – to burn, I can practically feel my phone melting against my face.

Cox has a place in north London, as well as a family home in New York, where he lives with his wife, Nicole Ansari, and their two sons. But we are talking by phone because he is still in Los Angeles, celebrating his triumph at the Golden Globes last weekend. He was named best actor in a TV series for his role on HBO’s Succession as Logan Roy, the oligarch who occasionally encourages but largely torments his four grasping, feuding children. The show (which was created by Peep Show’s Jesse Armstrong and will shoot its third season this year) is brilliant on wealth, media tycoons and corrupt dynastic families and feels breathtakingly of the moment. But the smart writing and acting make it timeless. Cox’s performance as the inscrutable then suddenly, terrifyingly, raging centre of the family already feels definitive.

Yet when his name was announced last Sunday, he was shocked. “Well, you never know with these things, do you? I thought I was maybe in with a chance, if only from a longevity point of view,” he says with a low rumble of a laugh. At 73, he will celebrate 60 years in the business next year. “I’m just surprised I’m still standing, I really am,” he says.

Afterwards, he celebrated his win – and Succession’s win, which was named best TV drama – by “taking lots of selfies”. Elton John paid his respects: “He was very praising of my Churchill, which was kind,” says Cox, who played the PM in the eponymous 2017 film. Leonardo DiCaprio also stopped by to tell him: “I’ve always wanted to work with you.” “Well, you’ve taken long enough about it,” Cox growled back. Has Cox always wanted to work with DiCaprio? “Mmmm, I don’t think in those terms,” he says affably.

Mainly he celebrated with the cast, even giving Kieran Culkin, who plays Cox’s onscreen son, a big kiss on the mouth as he went up to get his award. “I’m close to all my boys. We’re very family-like, which is ironic as we play such a dysfunctional family,” he says.

I ask if that closeness makes it harder for him to torture them on the show, such as in the infamous “boar on the floor” segment, when Logan makes family members scrabble for sausages.

“No, I love being nasty to my children!” he cackles.

Such is Succession’s popularity that Logan Roy has become something of a fashion icon. The style press loves his power cardigans, I tell him. “Ha! It’s all such bollocks, what [playwright] David Storey would call ‘a soulless stirring of the pot’.”

Given that Cox is one of Britain’s most prolific actors, celebrated as much for his theatre work (he won an Olivier in 1988 for Titus Andronicus) as he is for his TV roles (Nuremberg, Deadwood, Bob Servant Independent) and film successes (Manhunter, Braveheart, Super Troopers, The Bourne Identity), it would be ludicrous to describe this as his moment. Even in his relatively small roles – as the disapproving headmaster in Rushmore, say, or the terrifying writing guru in Adaptation – Cox has always dominated the screen. But Logan Roy has caught the public’s imagination in a way that feels new to him.

“It’s astonishing how much audiences love Logan’s cruelty,” he says. “I think it’s a reflection of the state we’re in. All of our moral certainties have gone by the wayside with the elections, with the Etonian twit in the UK and the pink Pinocchio in the White House, and you feel you can’t do anything about it. It’s like with the impeachment: it’s so clear that [Trump] is a bad man, but the Republican senators say: ‘No, it’s not this, it’s that’, but it’s all bollocks. He’s a horrible human being and he’s fucking everything up and he doesn’t give a shit,” says Cox, palpably only just warming up.

As Logan Roy in Succession. Photograph: Home Box Office/Graeme Hunter

Cox is a Labour supporter who has campaigned for Scottish independence. So he wasn’t wildly impressed with the results of last month’s election. “Ach! The Brits are so feudal. They don’t listen to a civil servant like Jeremy Corbyn, but they will listen to a windbag Tory like Johnson. And my country has suffered for it,” he says.

I have heard that Cox is a fan of cannabis so I ask if that helps him cope with the political situation in the US and UK. There is a long pause and I worry I’ve overstepped a line.

“It’s absolutely great and I recommend it to everyone – get stoned!” he says with deep feeling. “It does make the politics easier to bear. It’s a way of dealing with idiocy.”

Has he always been a stoner? “I didn’t start until I was 50,” he says. “I was very against it, actually. You know, I got married at 21 to an upper-middle-class English girl – well, with Scots parentage, but you know English Scots are the most English! Hahaha! We had two children, one went to St Paul’s, one went to Cheltenham Ladies College. It was all done proper. It wasn’t who I was, but happy wife, happy life. Then when I was 50, I realised I missed out on what was going on with young people because I was so square, and I was working so hard, I needed something to relax. So I discovered the wonderful world of cannabis.”

There have been inevitable comparisons between Logan Roy and Rupert Murdoch, despite Cox’s denials (“Rupert Murdoch has fuck all to do with it, and you can quote me on that,” he barked at the Golden Globes). But it must be strange for him, having played a media tycoon now for two seasons, to see the ongoing dominance of Fox News in the US, or to watch Michael Bloomberg’s bid for the presidency.

“Yeah, it’s interesting. All these guys, whether they’re liberal or the opposite, they see themselves as leaders. And they all have their own problems – clearly, because we’re suffering because of their problems! We’ve suffered under the hands of the Murdoch press and Conrad Black and now Donald Trump.”

And yet despite the show depicting how extreme wealth corrupts extremely, it has accrued fans among that demographic. Cox was recently in a cafe in Primrose Hill, north London, when he was approached by a man who told him that he and his wife liked Succession, “but she found it a little hard to watch sometimes”.

“Who’s your wife?” asked Cox. “Elisabeth Murdoch,” he replied. “Can you go a bit easier on her next season?”

“I said: ‘I’ll try,’” says Cox.

Murdochs aside, the family most reminiscent of the Roys are the Trumps, particularly the children. “There are certain similarities. You know, entitlement is just such an awful thing, and it’s the same in our country with [Prince] Andrew. I mean, what an idiot, what an outstanding dumb fuck: ‘I don’t know who that young woman was, and I don’t sweat.’ It’s ridiculous! I’m so cross with the idiocy of what we allow. It just shows how ridiculous the notion of monarchy is,” he says.

So I’m guessing he’s not a fan of The Crown, I say. There’s another pause. “I love it!” he says, and makes a loud guilty laugh. “I resisted it for ever and a day and then I started to watch it and it was like heroin. I was completely hooked – and that’s how they get you.”

Jesse Armstrong wove some of Cox’s biography into Logan’s, making the character a native of Dundee and even shooting some scenes in Cox’s hometown. Like Logan, Cox has a daughter and three sons from two marriages and, also like his alter ego, his childhood was unimaginably different from the one he was able to give his kids.

“That’s where Logan and I cross over, we really do. It’s very hard for [my children] to understand certain things, it’s just one of those things. My kids don’t have the Roys’ sense of entitlement, thank God, because we’re not that rich. But we had a holiday in London and we went to the Savoy for Christmas lunch and it cost a few shillings – I didn’t get that as a boy,” he says.

Cox was born and raised in Dundee, the youngest of five children of a butcher and a spinner. The family was always poor but when Cox was eight their situation worsened immeasurably after his father died from cancer. Soon after, his mother had a severe nervous breakdown and was given electric shock treatment. From the age of 10, Cox was largely raised by his sisters and on some nights, there was so little food in the house he would go to the local chippie and beg for battered scraps.

“People who don’t know poverty haven’t lived, quite frankly. You know everything is conditional,” he says. To this day, he has a bigger wardrobe than his wife because he is a terrible hoarder – after growing up with nothing, he can’t bear to give anything away.

Cox stumbled through school, leaving at 15 with no qualifications. He worked as a stage manager (“Worst stage manager ever – I always left the iron on”) before going to Lamda to study acting.

“When I came to London as a student in the 60s, it was a great period of social mobility,” he says. “It was in the wake of John Osborne and the angry young man, the rise of people like Albert Finney and Peter O’Toole. And that’s a legacy I’m so proud of, that I was at the tail end of. I was given a grant and had my expenses paid, and I was grateful for it. And now it’s like that never happened. I think it would be bloody impossible for me [to become an actor] if I were starting today. The tragedy in the UK is there’s a whole working class that is being removed from the culture.”

I ask what he thinks about the arguments over whether British acting is too dominated by posh people and he jumps in before I finish.

“You can’t blame Damian Lewis or Eddie Redmayne or whatsisname, er, Benedict Cumberpast, er, Cumberpat, no, Cumberbatch – that’s it,” he says. “You know, talent is talent and one has to be careful about not being mean. But it says something about our creative work that we haven’t got an even playing field. Egalitarian thinking is completely lacking in the UK,” he says.

This lack of egalitarianism sparks another thought. There is a brief cheeky “Shall I tell this or not? Yes, I shall” hesitation.

“You know, when I was a young actor I was touched up by Princess Margaret,” he says.

Brian, I am going to need more details on this.

“I was at the Royal Court. I was doing a play with Alan Bates and it was my 23rd birthday and I’d been given a red shirt from Lindsay Anderson. I’d just washed my hair so I was sort of glistening, heh heh heh, and I walked in and was introduced to her. She put her fingers on my shirt, and said: ‘This is a lovely shirt.’ And she started to run her fingers down the inside of my shirt. And I went: Uh oh! What do you do when you’re being touched up by a royal?”

What do you do?

“It was so funny. James Bolam, he could see what was going on and started going ‘Ooooh’ out of the side of his mouth, which somehow said princess didn’t take in at all. She just kept saying: ‘You were so wonderfully hooded on stage. I wanted to know more about you …’ She was an extraordinay creature. I excused myself and said: ‘Thank you, ma’am,’ and it came to a natural end.”

What an amazing man Cox is, working his way up from begging for scraps in Dundee to the absolute top of the Hollywood tree ( “I know, I must write my memoir”). Even his Brooklyn apartment is so smart that the New York Times once did a whole article about it. This included the memorable detail that he and his wife have separate bedrooms and a studio that they “tryst in”. Is this true? He has a shag room?

“Yeah! We do. The problem is in New York City it’s bloody hard to find the space. But it’s basically her room and I’m allowed to visit occasionally, heh heh heh,” he cackles in a manner that is, undeniably, deliciously, Logan Roy-ish.

Succession will return to Sky and NOW TV in 2020 and is available on Sky Store now