In a New Statesman competition in the early 1970s asking for the unlikeliest authors of previously published books, the winner was My Struggle by Martin Amis. The gilded youth, son of Kingsley, published The Rachel Papers at the age of 23, rapidly followed by Dead Babies and Success, before becoming literary editor of the magazine that dared to mock him. The son of the famous father had, said the cynics, enjoyed a rocket-propelled path to literary glory.

But 40 years on from his first novel, Amis suggests his resonant name damaged his career, and wishes he had put "greater distance" between himself and his father. "It's become something of a burden," he tells John Wilson in a wide-ranging interview to be broadcast on 20 July on Radio 4. "The Amis franchise is starting to get people down. Subliminally they think I was born in 1922 and wrote Lucky Jim when I was six. Life would have been simpler without him."

Amis, who will be 64 next month, has had an increasingly fractious relationship with critics since the mid-90s, when his insistence on a £500,000 advance for his novel The Information led to a parting of the ways with his publisher Jonathan Cape, his agent Pat Kavanagh (ditched in favour of so-called "super-agent" Andrew Wylie), and her husband Julian Barnes, a longstanding friend of Amis. Suddenly Amis, rather than his work, was the story, and that is very dangerous for a writer. The public may read about you, but will they still want to read you?

He now regrets not accepting Cape's original offer of £300,000. "The person who wants a quiet life, which is 90% of me, should have taken the Cape offer, and that would have been the end of it. These things stay with you. For years it was the number one thing people asked about, and it was not my finest hour." But he resents the accusation that he wanted the money for expensive cosmetic dentistry. "They [his detractors] talked about it as if it was a boob job, a procedure of choice, but I had absolutely no choice about it."

Amis says the death of his father in 1995 and his divorce from Antonia Phillips at around the same time – another drain on his finances – clouded his judgment, and that he was shocked to receive the letter from Barnes terminating their friendship. "It was naive of me not to anticipate it," he says. He and Barnes patched up their differences a decade later.

In recent years, Amis has become more celebrated for his interventions in public life than for his novels. He knows this, too, is dangerous for the writer – he likes to quote Gore Vidal's observation that fiction is written with the right hand, essays with the left – but is unable to resist the temptation. In the wake of 9/11, he told a journalist he was tempted to say all Muslims should suffer until they got their house in order. The qualification in his statement was quickly lost and he was consumed by controversy, with the literary critic Terry Eagleton eagerly leading the assault.

"It was a foolish and mischievous thing to say and I regret saying it," Amis tells Wilson. "The journalist who extracted those lines from me had just flown out from London to New York and was not allowed to take a book on the flight. No one was allowed to take a book. That seemed to me a terrible symbolic defeat. What a triumph for ignorance, stupidity, blinkerdom. It was a spasm on my part."

He has no such regrets over his statement in 2010 that the "silver tsunami" of elderly people needing healthcare threatened to overwhelm society and emasculate the young.

"It's going to be the biggest demographic change in the history of the world. The subterranean dialogue in government throughout the west is how are we going to pay for the old? And the only way to do it is to tax the young. I was in fact paraphrasing a paragraph from my novel The Pregnant Widow, which is why it comes out satirically [he talked of "euthanasia booths"]. But I don't regret saying it. I don't want my children to spend their lives slaving to maintain an elderly population."

In the interview Amis describes the murder of his cousin Lucy Partington by Fred and Rosemary West, and the difficulties of writing about it in his memoir Experience, published in 2000.

"It was a great challenge to even assimilate it, it was so dreadful. One of the awful things was that people would say 'How did she fall in with the Fred West crowd?', and she couldn't have been less [likely to]. My sister who, alas, has been long dead, might have ended up in there, as my mother often said, but not Lucy, who was very religious, unawakened, very serious, a good poet. The idea of that sweet, introverted girl realising what she'd done [when she accepted a lift from the Wests]. Her blood must have turned gangrenous."

Amis says writing the memoir helped him come to terms with his cousin's death – her fate was revealed more than 20 years after she had disappeared – and helped her brother David, too, but he still feels uneasy about it. "I did get permission from my aunt [Lucy's mother], but I don't feel entirely that I should have written about it. It was a great trauma for my imagination."

The interview with Martin Amis will be broadcast on Meeting Myself Coming Back on Radio 4 at 8pm on 20 July