Dennis Hopper might have been turning in his grave if he knew that the key guest of the Dennis Hopper season at the British Film Institute was Peter Fonda. After all, he barred his Easy Rider cohort from his own funeral.

Fonda recalls, "Well, I knew that Dennis was dying and I made many attempts to see Dennis as did Bert Schneider [the Easy Rider financier]. But he refused to see us. The funeral service was in a chapel in Taos, New Mexico. I rented a private jet and flew in, but I was not allowed in the chapel. So as much as I wanted to pay my respects, to Dennis and his family, I was not allowed to be a part of it."

It's yet another sad ending to the Easy Rider story. As Fonda explains it, their dispute was over who should get the writing credit and how the share of Barbarella screenwriter Terry Southern's should have been divided when he dropped out of the project. "My contract with him was the same, he just felt that he deserved to have that. He got millions from me that he misappropriated investing in phony gold mines. That's his problem. I mean, it's a shame, because he was too whacked out on drugs. I just think that he was so caught up in his own megalomania and his own bitterness that he couldn't see that I treated him quite fairly and that I respected his genius and his work."

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The 74-year old laughs heartily at the irony of all these money problems coming from a movie that was supposedly about not caring about money. He says, "I find it amazing that Columbia insists that Easy Rider has only made $19m, I know what I got, I know what my percentage was, I can do the math, it's really simple."

Fonda was also known for his drug taking, famously taking LSD with The Beatles and Nancy Sinatra. "I'm a pot head," he chirps. "I do it at night when I'm going to sleep. I don't have the desire to do speed or coke, I already talk too much. LSD I don't need to do it again. I'll do the magic mushrooms. I love to laugh and they make me scream with laughter." Formerly a big advocate of LSD, he says of the drug today, "That drug was miraculous for me, but I see a psychiatrist now. I think it's much better to talk to him than take LSD."

Fonda belongs to one of the great movie dynasties. His dad was Henry, sister Jane, and daughter Bridget. It's a fact that he's reminded of every time he calls one Easy Rider co-star Jack Nicholson. They first worked together when Nicholson wrote the script for the Roger Corman-directed The Trip. "I don't see Jack so much, every now and then I'll call him. His houseboy answers the phone and I say, "Tell Johnny Hot that the Patrician is on the phone!' Because Jack would say, you are, Fonda, you're a Patrician, far out.

Nicholson surely recognises that the man who seems most important in his former colleague's life is his father, Henry. Even his biography is titled Don't Tell Dad. He crops up several times when Peter talks. When I meet him he's wearing antique Persol wraparound sunglasses that were given to him by his optometrist. "I had a fascination with General Douglas MacArthur and his aviator lenses, so I started wearing them when I was 13 to piss my father off, and I just kept wearing glasses," he says. Later, explaining his desire to be the best artist he can, he posits, "If I wasn't an actor and I was digging ditches, let me tell you that I'd be digging the best ditches. People at the other end of the ditch would be looking over and saying, 'Do you know who that is? That's Henry Fonda's son.' Fuck that, that's who they see me as. If I'm on stage, if I'm on film, I'm not Henry Fonda's son. I can't duck my lineage. I can't denounce my father, my name is Peter Henry Fonda, that doesn't mean that I have to be like him."

Some of his antagonism comes from the fact that his dad told him that his mother had had a heart attack in 1950 and died. In truth she committed suicide. He found out the truth a decade later. Hopper made him relive the story on camera in Easy Rider, despite Fonda's protestations. "I wanted to cut that out of the film and everybody else convinced me not to do it, it's so personal and the character Captain America is my dream, not my youth. Others say it's such a raw moment. But I didn't fight with Hopper, we went back and forth, and ultimately he said he wanted me to do it because he was the director. How could I argue with that?"

He speaks in that same beguiling enigmatic manner of Nicholson. It's impossible not to be find him endearing. Every word had me hanging on for more. He admits that interviews are, "a performance, because I have to be sharp, say things that are not too provocative but interesting enough that you want to see the film I'm promoting. I'm performing Peter Fonda." As if to prove the point he adds, "You don't do it by being a bump and a log. If you've ever had to interview Harrison Ford you know what it's like to interview a bump and a log. I love him but he's a cabinet maker."

There's also the impression that he didn't have the career that he should have given the success of Easy Rider. It was Hopper and Nicholson that went on to have other iconic roles. Despite directing three films in the Seventies, it's often said that Fonda dropped out of Hollywood. "OK, in '73, I starred in Dirty Mary, Crazy Larry, that made a shit pile of money. More money than any film Dennis ever made. It's just that Hollywood thought that I had come back when I made Ulee's Gold," he says about the beekeeper role that saw him garner a Golden Globe and Oscar nomination. "I've made 70 films, did theatre, maybe I'd have two or three months off, but I always worked. People thought that because I bought a sail boat, lived on a boat, I didn't own any property, they thought that I was sailing stoned out of my head."

Had he taken drugs and sailed he said he would have had an accident and be dead. Nor if he dropped out would he be able to afford to live on a ranch in Montana where he now lives with his third wife.

He explains, "That Dennis and Jack had their careers didn't affect me at all. I know Hollywood didn't like me. They blamed me for what they thought was trying to overthrow the system. My reaction to that is are they kidding me? The government yes, Hollywood no."

In 2011 he took part in the documentary The Big Fix, which slammed the Obama administration's handling of the BP oil spillage in the Gulf of Mexico. "Allowing companies to tell our law enforcement or coast guard what to do. Excuse me you don't do that. And yet I see my government, I see them allowing this to happen, and not fighting strongly for the American people. What are we doing in the Middle East fighting religious wars? Somehow the energy lobby is so big that Obama can't break through it. And that's what's happened to our politics, it's become the best government money can buy."

He remains outspoken, but he also remains tremendously busy, and is currently shooting three projects back-to-back, he's playing Nic Cage's father in political drama The Runner, is starring alongside Bruce Dern in thriller Borderland, and has just shot a pilot for Galyntine, a TV show being produced by Ridley Scott.

Dennis Hopper: Icon of Oblivion, BFI Southbank, London SE1 (020 7928 3232) to 31 July. Dennis Hopper 'The Lost Album', Royal Academy, London W1 (020 7300 8000) to 19 October