One of the early big laughs in the Broadway musical Dirty Rotten Scoundrels — now in the West End and starring Robert Lindsay and Rufus Hound as a couple of con men targeting rich women on the Cote d’Azur — is delivered by the song Great Big Stuff. The singer is Hound’s vulgar American grifter Frank (Lindsay plays an Englishman) who is listing the things he would own if he could afford them. Frank wants a Zamboni, which apparently has American audiences gasping for breath so funny is the line.

“It got a giant laugh in New York,” says David Yazbek, the man who wrote that and every other lyric in the show, as well as the music. “No one in England knows what it is.” Should you care, a Zamboni looks a bit like a combine harvester without the thresher and rejuvenates the top layer of ice in ice rinks. But it matters not as the word has been cut from the West End version in the tailoring of the show to the British market.

The composer, singer/songwriter has just emerged from the dusty basement of his New York home empty handed. He was searching unsuccessfully for his college copy of Much Ado About Nothing as he’s writing the music for a forthcoming Central Park production of Shakespeare’s comedy. As he dusts himself off, Yazbek says he thinks Zamboni became “Guccioni on the phoney” for London. But as he agonises over every syllable in his scores — which also include the musical versions of The Full Monty and Women on the Verge of a Nervous Breakdown — replacing a lyric “is to torture myself over something I’ve already tortured myself over”.

Listening to the seemingly effortless wit of his lines, you would never imagine the torture involved. The songs he writes for himself — what he calls the music from his soul — have a wry take on city life and sometimes even politics. But the songs he writes for the theatre reflect the life and attitudes of his characters. As dirty rotten scoundrel Frank would put it, Yazbek’s is a “life of taste and class, with culture pouring out his ass”.

Yazbek is one of the very smart Jewish composer/lyricists who are typical of the talent on which so much of New York musical theatre is built. It’s a list that includes Jason Robert Brown (Parade) and Adam Guettel (The Light on the Piazza), the grandson of Richard Rodgers. From a London perspective, it’s easy to imagine these writer stars hanging out together in Greenwich Village coffee shops and being generally brilliant, smart and, well, Jewish. Yet it’s only a bit like that.

“Jason and I are on each other’s Twitter feeds,” Yazbek says. “He’s a fan of mine and I’m a fan of his. Adam Guettel is a very close friend for a long time. We were in a band together when we were both in our early 20s. He played bass and I played guitar.”

But it would be wrong to paint Yazbek in the mould of the old school Jewish Broadway composers — the Gershwin brothers, Rodgers’s collaborator Lorenz Hart, Leonard Bernstein, Stephen Sondheim, John Kander and Fred Ebb (Cabaret, Chicago), Charles Strouse and Stephen Schwartz (Godspell, Wicked), to name a few on a very long list. “It’s a fascinating thing to look at,” says Yazbek. “I don’t know why the hell this [New York musical theatre Jewish culture] is. But I think it’s changing. I’m not enough of a student of musical theatre to say who is a Jew or who is not. But I’m only half a Jew,” he adds, even if the Jewish half is his mother.

Fiftysomething Yazbek describes himself as culturally Jewish, with religious Judaism holding little interest. “I studied Zen Buddhism pretty seriously for about a dozen years. That taught me a lot. But even saying it bothers me because I don’t like labels. Though I probably know more about the Old Testament and Judaism than most of my friends who actually did go to Hebrew school. That knowledge came from a strong curiosity about faith and spirituality. My mother’s side came over from Russia and my father is totally Lebanese. It’s a hash of semitic genes.” What he calls “the gift” that blossomed from those genes showed itself early on.

“The gift that I have musically tends to be the one you don’t really cultivate — the ability to come up with melodies that are memorable. There are so many people out there who are amazingly talented and wonderful. But they just can’t pull a melody out their ass. And the other gift that I think I have is time. It just has to do with the groove. Even as a three-year-old I remember really understanding groove. I remember being a kid and hearing some salsa band and understanding intrinsically why this was working. And then hearing a certain Afro-Cuban groove and understanding why that was different, why it was exciting and what it was doing. That’s in your blood somewhere.”

Away from Broadway, Yazbek has his own band that straddles jazz and rock music. He’s so at home with diverse musical forms — he’s produced for British indie group XTC and written award-winning American TV theme music — that his band could be a mix of Scottish bagpipes and South American panpipes and it would still get a following. The lyric writing is not so easy. “Lyrics are really hard to do. Melody just seems to kind of come to me. If I could find a lyricist that I really thought was great I’d have such a less stressful life.” But for the moment the stress remains. If Dirty Rotten Scoundrels is as successful here as it was in New York, he will have two West End shows in London when Women on the Verge of a Nervous Breakdown opens in the West End in January. And he’s currently writing the music and lyrics to more musicals — or “titles” as he likes to call them — than most people see in a year.

“I’m writing one big title. I can’t tell you what it is, but it’s hopefully going to be funny. I’m writing one title that’s going to be smaller and more heartfelt. I’m doing the lyrics to a show about a famous female televangelist and I think the one I’m most excited about is the one that [Scoundrels book writer] Jeffrey Lane and I have been bouncing back and forth but which we really haven’t had time to start.”

If he does have two West End shows running simultaneously, London theatregoers may get a chance to see Yazbek perform. “Yeah, maybe I’ll come over and do a few shows,” he promises before disappearing back into his basement to search for his copy of Much Ado.

Dirty Rotten Scoundrels is at the Savoy Theatre