The first restaurant David Baddiel suggests for lunch turns out to be fully booked, so we go somewhere else. He's not the kind of person to pull the "Don't you know who I am?" stunt. He finds fame slightly awkward – a litany of "small, minor humiliations", such as the time he visited Auschwitz and became aware of a man standing next to him.

Baddiel presumed the silent stranger was deep in contemplation about the inhumanity of man. Instead, after a few minutes, he chirped up with: "Dave, when's Fantasy Football coming back?"

"You realise," says Baddiel, 49, when we sit down at Umu, a Japanese restaurant in Mayfair, "that people think they know you … because as far as they're concerned, you're, on some level, a mate of theirs."

The Auschwitz incident is one of many Baddiel explores in his new standup show, Fame: Not the Musical. It is his first full show for 15 years and so far, the critics have loved it. "Which is unusual for me," says Baddiel, ordering the tasting menu for both of us.

The first course arrives: Cornish squid with tosazu and ginger. Baddiel devours it so quickly it's almost as though he's afraid the waitress is going to swipe it away before he's done. When I make a comment about sushi being the kind of food that never makes you feel full, his eyes glimmer. "Watch me," he says.

Fame: Not the Musical came about because Baddiel realised no one talked honestly about the mundane awfulness of a certain level of celebrity. "There are two main tropes of fame," he explains. "One is that it's all glittering baubles and Simon Cowell says it's what we all want. The other is the Amy Winehouse, Janis Joplin route: the tragedy of the empty hotel room. But then there's the third way."

This is men driving vans who shout out of their windows: "Oi, Baddiel!" It's the fellow passenger on a Ryanair flight to Krakow who accuses you of being "a bit tight" because you're trying to save seats for your children (this did happen). It's the repeated occasions you're mistaken for Ben Elton simply because you wear glasses and are a bit beardy.

"There's this pre-existing idea of me as a laddish, up-himself bloke who talks loudly in a 'north London drone' and none of it is true," he says as the waitress delivers a bowl of soupy, salty deliciousness containing Ibérico pork and Chinese cabbage. "I don't think I've been changed very much by fame. I'm not a very changeable personality."

If he's not that loud-mouthed bloke from The Mary Whitehouse Experience or the one who sang Three Lions with Frank Skinner during Euro 96, then who is he? A thoughtful lunch companion, as it turns out, with an above average fear of his own mortality, which leads to a prolific rate of work.

As well as the new standup show, Baddiel is adapting his 2010 film The Infidel into a stage musical, creating and hosting a panel game for Radio 4 and developing a pilot for Channel 4 entitled Sit.com, which looks at the impact technology has on family life. "I'm interested in it on a mundane level. It's about me sending an email to Morwenna [Banks, Baddiel's partner and fellow comedian, with whom he has two children] to say 'Lunch is ready' rather than just going into the next room and telling her.

"John Updike," Baddiel continues, dropping the name casually into conversation as only someone with a Cambridge double first in English can, "who is basically my hero, thought it was his job to 'give the mundane its beautiful due', which is it, really. I don't think 'What would Jesus do?' I think 'What would John Updike do?' "

Plus, Baddiel is Jewish – although judging by the swift work he's making of the Ibérico pork, not particularly devout. His Twitter biography states simply: "Jew" and it is clearly a key part of his own identity.

As we're presented with a spoonful of Exmoor caviar (for such a thing does indeed exist), Baddiel says he believes there is a kind of "unconscious racism" directed towards Jews in Britain. In 2010, he and his older brother, Ivor, made a short film called The Y-Word that challenged the acceptability of fans chanting "Yid" at football.

Baddiel recalls that "a very famous person" said to him that "Yid" was in no way as offensive as the n-word. When Baddiel asked why, this person replied: "Because the Jews are rich."

"People think Jews are basically rich, basically in control," he tells me. "That's a) incredibly patronising to black and Asian people and b) it doesn't matter – history has shown they get massacred."

Baddiel's maternal grandparents were refugees from Nazi Germany, arriving in Britain in 1939 when his mother, Sarah, was a baby. His grandfather was "in and out of mental homes with depression because all his family had been killed". He describes his mother, with great affection, as "fascinatingly mad". His father was from working-class Swansea and became a research chemist for Unilever.

Baddiel grew up in Willesden, north London, the middle of three brothers. It was "a very ordinary, lower-to-middle-class upbringing". His younger brother, Dan, is now a cab driver in New York City. He tells me proudly that Dan was chosen as "Mr February" in the 2013 New York Cab Drivers calendar.

To this day, Baddiel votes Labour, "mainly because my MP is Glenda Jackson and I remember once hearing her say that the thing she was proudest of in her life was being on Morecambe and Wise."

Food was not a major part of his childhood. "My mother, bless her, was a terrible cook," he says. "She used to cook really weird stuff. She did chicken soup but it was this huge vat of water with a claw in the middle and she'd leave it for a month on the hob. We had a grill with fat on it from before the war.

"I don't remember tasting anything nice at all until I was about 17 when my mate gave me half an avocado … It was like an epiphany."

He confesses he's a fairly limited cook himself – his signature dish is cod in a peanut butter sauce designed to mask the flavour of the fish.

"I don't really like fish."

But David, I say. We're in a sushi restaurant at your suggestion.

"I like raw fish. It's cooked fish I have a problem with. I think it's one of those things you have to be properly grown-up to enjoy, like reading non-fiction. Every time I'm in a restaurant, I think 'I'm quite old now, I should have the fish' and I always get it and I'm always disappointed."

His favourite cuisine is Indian – the older he gets, the more he worries his tastebuds are dying and the hotter he wants the spicing. There's a restaurant near his house that has developed "Chicken Baddiel": butter chicken spiced to within an inch of its life.

Back at the table, we are nearing the end of our mammoth tasting menu. Outside, the skies have turned dark.

"I didn't want to interrupt but do you realise there's been some sort of major incident outside while we've been having lunch?" Baddiel asks.

I turn to look out of the window. Policemen are cordoning off the street.

The next day, I will read in the paper that two men on scooters were apprehended as part of an attempted jewellery heist. Baddiel had seen it all, but had been too polite to mention it. And there was also a part of him, I'm sure, that hated drawing more than necessary attention to himself.

After he'd left I realised I'd forgotten the crucial question. I still don't know when they're bringing back Fantasy Football.

Fame: Not the Musical tours the UK from 31 January; davidbaddiel.com