"What the show likes to do, like all body swap stories, is get as much comic juice as possible out of being the opposite of what you thought you were," continues Baddiel as he makes inroads into a classy salad bought from the local market. "It heads towards a place which I believe optimistically to be true, which is that actually Muslims and Jews have much more in common than what we don't have in common - theologically, culturally, socially, historically. We lived perfectly harmoniously for many years in parts of the world before now."
Then the optimism momentarily evaporates. "But yeah," he says, "it has got worse. It wasn't great in 2010. But the Muslim-Jew situation has got worse."
This isn't the first modern musical to consider religious identity. Jerry Springer did it in 2003 and The Book of Mormon is still doing it.
But although both of those shows lampoon religiosity, The Infidel is probably the first attempt to target the more intolerant reaches of religion, not only Islamic extremism but the hardening attitudes of Jews and Muslims towards each other. In that sense, it is tackling issues that have a lot of fear and loathing attached. That said, the one thing The Infidel is not is anti-religion, Baddiel stresses.
"It is a very juvenile aspiration to p*** people off because of their beliefs. We are not doing that. Not just because it would be very sixth form, but because it could get us killed. What we're trying to do is recognise what Muslims and Jews believe wrongly about each other, which is a much more complicated thing to do."
You can add to that, "make people laugh". Apparently the film is a big black market hit in the Middle East because central to the story is the depiction of an ordinary Muslim family in a way that is seen very rarely in the West.
"When I wrote it, Peter Kosminsky's Britz had just finished on Channel 4. It featured a brother and sister. She was an aspiring suicide bomber and he worked for MI6. I thought, 'That's leaving out a bit of a spectrum of humanity'."
Time will tell whether the musical version of The Infidel can bring together Jews and Muslims. The movie didn't, despite the fact that it is very funny. But perhaps that is too much to expect from what even Baddiel describes as a "small British film that punched above its weight". His main objective at that point was just to write a funny movie. It starred the British-Iranian comedian Omid Djalili as the Jewish-born Muslim Mahmud.
"The catalyst was seeing Omid perform at the Palladium and thinking, 'he could be Jewish', Baddiel recalls. "He's a hilarious performer and some of his rhythms are not un-Jackie Mason."
But maybe a musical has a better chance than the film in reconciling the two Abrahamic but estranged faiths.
As with the film, the cast includes Jews and Muslims. Among those supporting the central role of Mahmud, played in the musical by Kev Orkian (whose background is Armenian), is Jewish actor Andrew Paul.
Paul plays the role of black cab driver Lenny, Mahmud's Jewish enemy and then best friend. Mina Anwar reprises her film role as Mahmud's wife. The multicultural mix will help as, unlike cinemas, where people watch in the dark and leave, theatre imposes a sense of community on its audiences. At its best, it's like being part of a congregation. It's religious. So it's just possible that, for a couple of hours at least, Jewish and Muslim members of the audience will feel they have more in common than they thought. They'll certainly have the show they're watching, whether they enjoy it or not.
For Baddiel, much of the story may be primarily about a Muslim and his family, but the perspective was also very Jewish. "We were able to do a film about Muslims and Jews, but also a comedy film about what it is to be a British Jew and what it feels to be part of multicultural Britain." Not many, if any, films have done that. And certainly no major musicals. Baddiel holds dear the response he received from Howard Jacobson when the novelist saw the movie at the premiere. "He came up to me and said, 'This is amazing. What you've done is smash through the parochialism of British-Jewish film.'" From the reaction to the movie, it seems that many Muslims may feel likewise.
But when Baddiel wrote the screenplay, he was taking a risk. "I was writing more out of my comfort zone with the stuff about Muslim life and the jokes about Muslims. With Jews, I knew what I was doing ."
So the film was first shown to an invited audience of Jews and Muslims, partly to test Baddiel's judgment about what was, or wasn't, offensive.
"There were some Jews in the audience, but there were mainly Muslims, and some were hardliners. There were a lot of burkas, and a lot of slightly frightening looking fundamentalists."
Baddiel admits to being more worried about offending Muslims than Jews. "As I used to say in my stand-up, 'What are Jews going to do? Ban you from Carmelli's?' But it went down really well.
"I know this sounds like it couldn't have happened, but it did. A woman stood up and said, 'I have been dabbling with fundamentalism and I'm not going to any more because this movie has made me feel it's a load of rubbish'.
"It's taking the p*** out of extremists on both sides."
The Infidel - The Musical is at the Theatre Royal Stratford East until November 2
