There are two kinds of joke that characterise a Mel Brooks show. One is that, deep down, everyone wants to be in a musical. So, in this revamped version of his Broadway show (itself an adaptation from the 1974 film) Hadley Fraser’s serious brain scientist Dr Frankenstein — pronounced “Fronkensteen” he insists, to distance himself from his notorious grandfather — expresses his fascination with the most complex organ in the human body not with a lecture, but a lyric.

“There is nothing like a brain” he sings, to a tune that sounds something like There Is Nothing Like a Dame from South Pacific. And when the monster dons top hat and tails and lumbers as best he can while singing Puttin’ On The Ritz, you know that in his chest beats a heart that loves Broadway, even if it originally belonged to someone else.

The other kind of gag is shameless vulgarity. Frankenstein’s — sorry, Fronkensteen’s — uber wench lab assistant Inga (played by probably the best singer dancer in the country, Summer Strallen) is a big breasted and bouncy blonde bombshell. In fact, all of Brooks’s women here are ultimately defined by sex.

Sure, Frankenstein’s (sorry, Fronkensteen’s) fiancée has the haughty air of an heiress, but eventually all she wants is “big love, deep love” which is apparently what the monster gives her after whisking her off to a cave against her wishes.

And, when Lesley Joseph’s corseted Frau Blücher sings her big number He Vas My Boyfriend, hers is revealed as a masochistic kind of love that has been beaten into her by an abusive man.

I mention this somewhat unfunny side to what is a downright hilarious show because a colleague was so offended by what she saw as old-school chauvinism (the kind that led to Harvey Weinstein’s alleged abuses, she says) that it set her against the production. If she has a point, it is perhaps more disturbing still that it takes a female reviewer to write about it. But does she? I’d say up to a point.

If Joseph’s Blücher has a sister, it would be Nurse Diesel from Brooks’s slightly later (and to my mind superior) comedy High Anxiety in which Diesel is the disciplinarian ruler of a psychiatric hospital.

She is revealed as someone with an S&M sexuality who, unlike Blücher is more prone to dishing it out. And, for that reason, she’s funnier. As James Corden recently found after telling some Weinstein jokes that were off-target, the aim of a joke has to be solely directed at those with the most power. Brooks of course, knows this. Or usually does. As for the other women in his show, they are as much a pastiche of thinly drawn female characters as the men.

Of these, British stand up comedian Ross Noble as Frankenstein’s (sorry, oh forget it) assistant turns out to be as terrific as Marty Feldman was in the original film. Actually, more so, because Noble has to include Broadway director Susan Stroman’s drilled-to-the-hilt choreography while dressed in a medieval cassock.

Young Frankenstein is not quite the monster hit of Brooks’s other stage-to-screen adaptation, The Producers. But it only has to be a fraction as funny to be the funniest show in town. It is. And Brooks, who was in London for the revamping, shows that, at 91, his genius for comedy is as brilliant as it always was. Almost.