“Hellooooo!” The nice folk at Gilgamesh have tucked Omid Djalili and me in a quiet corner of their restaurant, which is roughly the size of an aircraft hangar. This is, I assume, because they imagine we will want a tranquil spot for our interview and also because they think that much loved comedian and actor Djalili might desire to slip in and out of the premises undetected. On this second point, they seem to have erred. Djalili is now on his feet, waving his arms in the manner of a castaway trying to attract the attentions of a ship on the horizon.

“Hellooooo!” he bellows across the floor again. In actual fact, he would just like to see a menu. “Over here!”

Heads turn, but then celebrities and expressly celeb-spotting is kind of the point of Gilgamesh. Unprepossessingly located by the side of the train tracks above the old Victorian horse hospital in Camden, its opening in 2006 was rumoured to be one of the most expensive that London had seen. Stars, particularly from the B or C register and below, flocked. On Gilgamesh’s own website there are testimonials from Spice Girl Melanie Chisholm, singer Olly Murs and Aston Merrygold of JLS, who boasts of eating 16 pieces of salmon sashimi in one sitting.

Named after the Sumerian king, protagonist of the world’s oldest literary epic, Gilgamesh offers a gap-year ramble around Asia: sushi, dim sum, curry, noodles. It has been derided as more of a theme park than a restaurant.

Djalili has little truck with such snobbery. He first came a couple of years ago, on the recommendation of Tim McInnerny, his co-star in the West End run of What the Butler Saw. When the menu arrives, he announces that he would happily eat anything on it. “Definitely the steamed Chilean sea bass, that’s fantastic, the crispy black cod with mango sauce,” he says, perusing the set offering for £55 a head. “Let’s go for that and they’ll just bring everything for us.” Djalili is back on his feet again, scanning the floor for a waiter: “Hellooooo!”

Reticence has never been the 49-year-old Djalili’s thing. As we wait for our starters, we sip mocktails and he explains that he was born to be an entertainer. One of his ancestors was an “Iranian poet laureate” who was revered in his homeland until he converted from Islam to become a Baha’i, which is still Djalili’s faith. Along with a group of fellow converts, this poet was tortured and sentenced to death, but even then they did not lose their sense of humour.

“They were walking barefoot in the snow to be executed and they all just pissed themselves laughing,” says Djalili. “Their executioner said, ‘If you’re not taking this seriously, you can all fuck off.’ So they let them go.”

Djalili may have known from an early age that he was meant to be famous, but this destiny wasn’t so clear to everyone around him. Born and raised in west London, he had an undistinguished academic career, endlessly retaking A levels, but scarcely improving on a smattering of Es, Fs and unclassifieds. He had a spell as a chauffeur, secretly believing that he should be sat in the back of the limo. “I had this malaise in me until people knew who I was or could see what I was capable of,” he admits. “Then I could relax. Then I could be myself.”

The food starts to arrive on grand platters: broccoli steamed to perfection and cut with a citrus dressing; monkfish gently cooked in almost translucent tempura batter. It’s not hard to see why Djalili likes it here. He continues, “My dad once said to me, ‘We’re around boring people, so rather than complain about being bored, why don’t you do something to alleviate the boredom? Be the initiator. Sometimes it will go wrong and they will be offended, but 95 times out of 100, it’ll go well and people will remember you.’”

This memory inspires a deluge of anecdotes, many of which fall into the 5% of occasions where his attempts to entertain were misconstrued. There was the time when Russell Crowe thought Djalili was coming on to him on the set of Gladiator. Or, in his chauffeuring days, when he was driving Metallica to perform at Knebworth and lead singer James Hetfield, one of the more eccentric men in rock, declared, “This guy is crazy!” Djalili repeatedly cracked jokes about Prince Harry’s misdemeanours at events where Prince Charles had specifically requested he perform. “He asked me to emcee a few events for him at Clarence House,” says Djalili. “I think he’s moved on now.”

Perhaps the best story is when Djalili was introduced to Robert Redford on the film Spy Game. His eyes twinkle as he prepares to deliver the punchline; he knows it’s a good one. “I said, ‘Mr Redford, I’m a big fan. You were the best thing in Hawaii Five-0.’ And he sized me up and replied, ‘Why, thank you. You were great in Doctor Zhivago… but you’ve let yourself go.’”

Funny and fabulously indiscreet, Djalili would be hard to top as a dinner-party guest; he is also clearly passionate and knowledgeable about food. He grew up mainly eating Iranian dishes, prepared by his mother: “It’s bland, it’s meat, stews and rice, that’s all it was.” So it was a shock last year when he was asked to present a TV series about our growing infatuation with spicy food; disgracefully it was not called Djalili on Chilli, but Hot and Dangerous.

For a man who had rarely eaten chillis – “I thought they were like wasps. Things that exist but there’s no point to them” – Djaili acquitted himself admirably. On two occasions he ate the Widower curry at Bindi restaurant in Grantham, which is infused with 20 Naga Infinity chillis and scores more than six million units on the Scoville scale. “It nearly killed me,” says Djalili. “It’s like a nuclear bomb going off in your mouth. The first time I tried it, stuff came out of me from 1973 – seriously, it was really bad. Then the second time, the body knew so it held it. My anus said to the colon, “Can you keep it up there for about a week? Let the chillis dissipate and then it can come out.’”

The food keeps coming at Gilgamesh, though mercifully nothing that would cause a blip on Mr Scoville’s rating. Our main course is the steamed Chilean sea bass, served in a ginger and spring onion broth, with fried lotus root and tofu on the side.

Djalili says: “My relationship to food has always been difficult, because I’ve always been overweight and I’ve always battled it. I’ve tried a lot of diets, but I’ve come to one conclusion: I’m a fat git and I just have to accept it and try and manage it.

“If I’ve got to carry this bit of fat around my stomach for the rest of my life, then I apologise to my pallbearers,” he goes on, laughing. “I’ll be heavy when they carry my coffin.”

Eating healthily is especially challenging at the moment, as Djalili is 46 engagements through a 95-date stand-up tour, Iranalamadingdong. For a while Djalili and his team tried “the Jimmy Carr rule”: not eating after 6pm – the key to the comedian’s weight-loss of the past few years. But with long nights travelling up and down motorways, it has proved impossible to stick to.

Djalili weighs up whether to eat the desserts – a white chocolate and mint mousse and a coconut pannacotta – and decides it would be rude not have a taste. This leaves time for one final anecdote. On this tour, he is travelling in a people carrier, but on his previous one in 2012 he had a flashy bus, which had the internet and could play DVDs. The problem was that it made Djalili travel sick, so he ended up driving to shows in his own car. On the way to one gig, Djalili was stopped by the police: his driving licence had been revoked. In the previous weeks he had racked up a British record number of points.

Djalili’s eyes twinkle again; we’re getting to the good bit. “So there was a court case and the judge said, ‘Mr Djalili, you have 36 points on your licence and another 18 pending, you are going to be banned from driving. Do you have anything to say?’ And I said: ‘Can you give me a lift to the station, your honour?’”

Omid Djalili’s Iranalamadingdong tour continues until 28 March (omidnoagenda.com)