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It must have been a rich childhood, doted on by the three females and befriended by this deceptive father with his ferocious work ethic and quixotic jousts with the film industry. Look back over his impressive, bizarre range of post-Python films and you see tale upon tale of financial disaster sometimes followed by critical acclaim and eventual, slow-burning success: Brazil, The Adventures of Baron Munchausen, Twelve Monkeys, Tideland.

“Most of my films have disturbed people,” he says. “They are being taken down roads they don’t want to be taken down. That’s why they get angry. They go to films to be reassured – the car chase, the fireball, like pop songs they are comfortable with. One of the reasons I was never into drugs was that when kids in the Sixties were taking acid and telling me about their experiences, I would say, ‘Well, I see the world like that anyway!’ ”

This is something else that Harry has inherited. “It’s the same with me,” he says. “I once went on a classical civilisation trip with the school. I’d stayed up for days and nights and I was hallucinating. My parents asked me what I’d been taking and I said, ‘Nothing,’ which was true. I was just overtired and tripping out. I’ve never been interested in drugs because I can send myself away without any help.”

“But you’ve always been a little frightened when you start to go places,” says his father.

“Yes, it’s only recently I’ve started to accept that, and relax when it begins to happen, and wondered why I was getting stuck in a crazy, fakey world that I knew was going to scare me.”

What was it like, growing up with Terry Gilliam as your father? “Until recently, I always thought, ‘Oh, it [films] is just what Dad does.’ But the more I’m aware of his skill and ability, the more I think I can never compete with this – people saying, ‘Oh, he’s Terry Gilliam’s son so he’s got to be good,’ then saying he [Harry] isn’t as good as we’d expected.”

“Our expectations were always very low,” says his father with a good-natured laugh. It’s disingenuous and he knows it. It’s never really in the parents’ gift to lower the bar, is it? Not parents like the Gilliams. (His wife has had a highly acclaimed career in her own right, having met him in Python days.)

“I’ve always wanted the kids to find out what fulfils them. It’s terrible when the children of the famous and successful get lost. It’s hard to compete with your parents. Harder for boys than for girls, I’d say.”

Is Terry doing what all fathers are said to do, whether they want to or not – handing down what was handed down to them? “You mean, how to use a hammer properly?” If that’s what you mean. “My father was a carpenter. And yes, I did learn building skills, how to make things.”

“When I was younger,” says Harry, “I used to think Mum was more liberal than Dad, and now I realise this was not so. She used to try to guide me. She wanted me to be a medical psychologist because I like talking and listening and finding out what’s going on. So she thought that was my route. But I turned round and without telling her applied for art college, and when she realised, it was a bit late to do anything about it.”

But the father and son; they seem to have avoided serious conflict. Unless it’s all an act by two skilled professionals.

“We’ve had our troubles,” says Harry.

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