Musicals often go through many different reincarnations, even after they’ve made it big. Think of Candide or Cabaret or Merrily We Roll Along, shows that each received a full script overhaul (or three) in the years following their Broadway premieres. Composer Frank Wildhorn’s Wonderland was never a spectacular musical: the 2011 Broadway production, though crisply staged, good-naturedly tongue-in-cheek, and filled with witty theatre in-jokes, fizzled out less than a month after opening. But the UK tour adaptation, now stopping off at the New Wimbledon Theatre with a brand-new book by Robert Hudson, has taken that already flawed property and squashed it into pantomimic (but largely unfunny) one-dimensionality. This is one musical that desperately needs to be put back the way it was.

Wonderland 2.0 has become particularly flimsy and frequently incoherent because Hudson has squeezed an entirely different plot around the original production’s songs (although some bits have been rewritten at the expense of some good material). Maybe it’s because this version is targeting a younger audience than the original did, but there were real stakes in the Broadway iteration — in this touring production, when the Queen of Hearts cuts off people’s heads, they don’t even die; mortality’s not on the table in this Wonderland.

“You’re the person who can do the thing,” Alice’s hapless neighbour and eventual paramour Jack (Stephen Webb) tells her at one climactic moment, evidently as foggy about the plot details as the audience. Here’s a loose idea: Alice (Kerry Ellis) is an unhappy, urban single mother to Ellie (Naomi Morris), still clinging to the memory of her recently remarried ex. Alice, Ellie, and Jack wind up following the White Rabbit (Dave Willetts) down a dilapidated lift into magical Wonderland, where the tyrannical Queen of Hearts (Wendi Peters) reigns and an enchanted looking glass (amusingly voiced by John Finnemore) transforms people into another version of themselves.

Said looking glass converts timid Jack into a rock god, sweet Ellie into a brat, and the dotty Mad Hatter (Natalie McQueen) into a (very) temporary villain. What happens to Alice herself inside the looking glass is never quite made clear, but she does sing three ballads of self-recognition in a row once she comes out of it (“I Am My Own Invention,” “Once More I Can See,” and “This Is Who I Am”).

Wildhorn’s paint-by-numbers score, with lyrics by Jack Murphy, is actually cleverer than it sounds. The several pastiche songs, including those performed suavely by Webb and Kayi Ushe as the Caterpillar, were written to function as parody (and, given Wildhorn’s long, musically varied career, maybe as self-parody), send-ups of various pop genres and the musical theatre form. Now, plonked into the story inertly, these tunes just feel like lazy writing.

Luckily, though, director Lotte Wakeham has also assembled a cast of vocal powerhouses: Ellis, McQueen, and Peters all sing the roof off (the first two are former West End Elphabas). Ellis’ final number includes some truly impressive and emotional high belting (and she is charming in her scenes with young Morris throughout). McQueen and Peters both play crazy convincingly, the latter stopping the show with her high-pitched faux regality and vaudevillian flair (McQueen is saddled with delivering the unfortunate exclamation “Amazeballs!,” but elsewhere adds plenty of delightful wickedness to proceedings). Morris gives a vibrant portrayal of a girl forced to grow up too soon, and she has a lovely voice, as does Willetts, even wearing giant bunny ears.

Wakeham and choreographer Lucie Pankhurst ably keep things moving on Andrew Riley’s dynamic set. The eight-piece band under Alex Parker’s direction sounds excellent, but the blaring sound design means the loud speakers often render the singers inaudible.

In terms of good pipes, good looks, and gusto, the right ingredients are all there. There’s still a lot of this tour left, so maybe there’s a chance that, like this Wonderland’s headless victims of the Queen of Hearts, the brains can still grow back.

Wonderland is playing at the New Wimbledon Theatre until May 6.