One day in 1970 Ralph Steadman was out on a boat, covering the America’s Cup yacht race and feeling seasick. The illustrator’s companion on the waters off Rhode Island was the journalist Hunter S Thompson.

“Hunter was popping pills the whole time, and he was perfectly all right. I’d never had anything before. I said, ‘What are those things you keep eating?’ He said, ‘Well, they’re pills, Ralph.’ ‘What sort of pills?’ ‘Well, they’re psilocybin.’ ‘What’s that?’ ‘It just helps me through the day.’ ‘Would it be any good for seasickness?’ I said.

“This is where the phrase ‘Pay the ticket, take the ride’ comes from, because I took one. And, God, I’d never done drugs before or since. I don’t like them. I like wine, but not until seven o’clock at night. It’s all right as long as you know when to stop, like everything. The unfortunate thing with drugs is that once it’s in you it’s in you. Ain’t much you can do about it.”

Thompson, whom Steadman had met a few months earlier, at the Kentucky Derby, presented him with two cans of spray paint, one black and one red. They came up with an idea to graffiti one of the impossibly expensive yachts in the race. Now high on psilocybin, Steadman and Thompson debated what to write on its side. “Sheer lunacy, really . . . The funny thing is, the twisting of logic comes into play. ‘What are you going to write?’ Hunter said. ‘How about “Eff the Pope”?’ And he just said, ‘Are you religious, Ralph?’ It just sounds so funny now. I’ll never forget that line.

“He never really said his words properly. It was always ‘ruhhgh rughggh, Ralph’. If my name had been Trevor it wouldn’t have been the same. ‘Ralph’ was like a bark.”

In any case, Steadman says, the rattle of the spray can alerted a guard, who stopped them. Thompson panicked and shot off a flare – which then set another boat on fire.

“He was quite easy to be around,” Steadman says of the original gonzo journalist.

“They said you were weird”

Thompson’s first piece of gonzo journalism came out of that horseracing trip to Louisville: the landmark article “The Kentucky Derby Is Decadent and Depraved”.

How did that first assignment go? “We looked for each other for three days,” Steadman says. “Hunter had gone to the betting windows, saying, ‘Have you seen a weird guy? He’s not from around these parts.’ You know the way he talked. I had a little goatee beard at the time, and when Hunter saw me he said, ‘Excuse me. Excuse me.’ I turned around and he said, ‘Holy shit. They said you were weird – but not that weird.’ ”

According to Steadman, when the article was published Bill Cardoso, a journalist with the Boston Globe, called Thompson. “He said, ‘Hey, man, that was pure gonzo.’ Hunter said, ‘Gonzo? What’s gonzo? I like that word. That’s a good word.’ . . . I said I had to find out about that word. It’s a Portuguese word. It means ‘hinge’. I don’t know if many people know that. I guess it suggests ‘unhinged’. The thing about gonzo is, you go to cover the story, but you don’t cover the story: you become the story. That’s how it works. You get that involved in it and make your own story. We were going to go around the whole of America at one stage in the 1970s, just covering everything.”

Steadman and Thompson collaborated many more times, including in 1980 at the Honolulu Marathon. “We left shoulder to shoulder at a blistering pace, being picked up three miles down the road by a truck that took us all the way to the bottom of Heartbreak Hill, the last bit of the course in Hawaii. We were stood there – we had drinks – and said, ‘Run, ye bastards!’ as people came past. Of course our saying those things completely wiped our their energy, if you know what I mean. They got angry. We didn’t end up in fisticuffs, but shouting ‘bastards’ at the base of the hill, I mean . . . ”

Steadman trails off.

They also covered Muhammad Ali’s boxing match against George Foreman in Zaire in 1974, although their Rumble in the Jungle piece was never published. (In one account of their time there Thompson gave away their tickets to the fight; in another the tickets disintegrated in his pocket after he jumped into a swimming pool into which he had emptied a large bag of marijuana.)

Steadman’s drawings, which created a visual style to accompany Thompson’s words, were made famous by his assignments with the writer, and spawned countless copycats. Steadman’s work for Fear and Loathing in Las Vegas, Thompson’s best-known work – and, in fact, an assignment he didn’t accompany Thompson on – became iconic.

Steadman’s illustrations continue to permeate popular culture. There are his recent drawings of Donald Trump for New Statesman magazine, Louis Theroux’s My Scientology Movie poster, the cover art for Anthony Bourdain’s latest book, Appetites, the beer-label illustrations for Flying Dog Brewery, and Critical Critters, which is the third in a trilogy, after Extinct Boids and Nextinction, and is due later in 2017.

Last September the Society of Illustrators in New York held a retrospective of Steadman’s work, where the depth and complexity of his art expanded far beyond the gonzo years. His drawings can be an assault of splats and screams, visceral and brutal, or they can be calm and impossibly detailed, such as his 1983 book I, Leonardo – he also painted a replica of The Last Supper on a wall in his house – or The Big I Am, featuring stunning visualisations of God. There are also his illustrations for Animal Farm and his reimagining of the Alice in Wonderland stories.

Then there are more contemporary pieces, such as an incredible portrait of Bryan Cranston as Walter White, and his piercing political cartoons. “There’s a certain sadness attached to it,” Steadman says of the retrospective, “and that is the feeling that it’s all gone by. I can remember some of the aspirations I had at the time to change the world. I always say that I did change the world – and it’s worse now than it was when I started! . . . The older you get, the more sad, which is a shame. You’ve heard of Kurt Vonnegut. He’s a friend; I knew him well. He wrote me a thing that said, ‘Life is no way to treat an animal.’ So funny. He was a wonderful man.”

Steadman has a knack of balancing brutality with humour. There is as much clarity in his work as there is chaos, but it is all distinctively his. He created an aesthetic. How? “First of all it was a lack of being able to do it, actually, and wanting to do it,” Steadman says.

After growing up in north Wales, Steadman had set out to be an apprentice at an aircraft company near Chester, just across the border in northern England. He succeeded but tired of the repetition of factory life, so he left. (This upset his mother, who had been a shop girl for the TJ Hughes department store in Liverpool, where she met his father, a commercial traveller who sold women’s coats.) Steadman ended up working in a stockroom at a Woolworths back in Wales. One day, as he was sweeping, his old headmaster – “an awful man” – spotted him. “He saw me and said, ‘Look at you, sweeping the streets in Colwyn Bay.’ He sneered at me.”

Mr Fiddler

Steadman left and got a job as a tea boy at an advertising agency presided over by a studio manager called Mr Fiddler. “Dickensian,” Steadman says, laughing. Fiddler began giving Steadman things to do. Around this time, he says, he spotted an advert that said “You too can learn to draw and earn pounds!” “That was the Percy V Bradshaw Press Art School course. You had 12 lessons in how to draw, £12 for the 12 lessons, but for another £5 you could have six more lessons on how to be a cartoonist. My mother paid for this, and I did this course.

“It was a bit clunky, but they used to have people like [Leslie] Illingworth, [Carl] Giles, Vicky [Victor Weisz], all the great old cartoonists, and they gave lessons. It kept me going when I had to do my military service.”

He joined the Royal Air Force as a radar operator, which he says taught him how to watch television. In Devon with the RAF he drew the men and the boys playing cards but was conscious that he had no proper education in drawing.

After his military service his cousins Alec and Vera, who lived in east London, helped him find a room in a flat, and he went to East Ham Technical College for life-drawing classes, five nights a week and on Wednesday afternoons.

Steadman then secured a job in what became Thomson Newspapers. His first drawing appeared in 1956 in the Manchester Evening Chronicle, a riff on the Suez Canal crisis with a lock-keeper saying, “Nasser? Oo’s ’ee?” He met the cartoonist Illingworth again and asked for advice. Illingworth said, “The best thing I can say to you is: get the sack. Don’t become regular. Become freelance.” Steadman has been freelance ever since.

Something Ludwig Wittgenstein wrote stuck with Steadman. “ ‘The only thing of value is the thing you cannot say.’ If you have a drawing or see a photograph and you think, Oh, God, that’s what he looks like – or her or it or an animal – you know immediately what it means just by seeing it, rather than somebody trying to describe something to you, and you can’t get the hang of it. When you see it, it makes all the difference in the world. That became a guiding principal: explaining something.”

Approaching his work, Steadman discovered that he didn’t like pencil first and ink after, as many illustrators prefer. “People used to say, ‘Don’t you make a mistake?’ But there’s no such thing as a mistake, only an opportunity to do something else, change, adapt it as you go along. I’ve just been doing a drawing of Willie Nelson for someone, and I was showing it to someone and the ink was still wet, and it dribbled down the drawing. But it’s okay: I’ll pull it round somehow.

“I don’t like the second guess. I like taking the bull by the horns and going with it. Straight in there. Things happen, accidents happen, interesting things happen when you start drawing straight away into the white surface.

“One thing I love doing is slapping paint straight away on to a brand new piece of paper. There’s a great joy in that. Taking it from there. A lot of that goes on in the drawings. I’m not very fond of pencil.”

But mistakes do happen. On the advice of an agent Steadman sold the original drawings from Fear and Loathing to the publisher of Rolling Stone, Jann Wenner. “That is a big regret,” he says. But he has moved on.

Steadman’s drawings of animals are among his most tender; he speaks at length about the tragedy of animals being shot or species endangered.

You suspect he wouldn’t mind were some politicians to become an endangered species. When he began drawing them he regarded politicians as people who could protect the people they represented by turning social ideals into effective policy.

Should we therefore regard his political caricatures as evidence of a man who harbours a deep-seated resentment of what he sees as their failure? No, he says. “I can’t stand unkindness in people. People say to me, ‘Your drawings are bitter,’ but if there’s any bitterness it all goes down on paper. I’m not that person myself.”