Anyone drawn to this musical by the prospect of seeing Frasier’s Kelsey Grammer is in for a bit of a shock: although Grammer is the pivot of the story and the best thing in the show, he is off stage for long periods. For the most part we get a mix of father-son story and spiralling fairytale that never achieves the moment of ecstasy we look for in a musical.

The show has a complex pedigree. Daniel Wallace’s 1998 novel and Tim Burton’s 2003 film jointly inspired a short-lived Broadway musical in 2013. John August, who wrote the screenplay and the musical book, and Andrew Lippa, who did the music and lyrics, have tinkered with the Broadway format but the story remains essentially the same. Edward Bloom, a travelling salesman, has a stroke and recapitulates the tall stories, involving witches, giants, mermaids and circus showmen, he has long told to entertain his son, Will. As Edward approaches his end, the sceptical Will tries to come to terms with a father whose life seems to have been built on exuberant fabrications.

Fails to exploit … Big Fish: The Musical, with Colby Mulgrew, Jamie Muscato and Kelsey Grammer. Photograph: Tristram Kenton/The Guardian

I am not sure that right now the world needs a paean to a narcissistic fantasist like Edward, whose idea of a joke is to hijack his son’s wedding by announcing that the bride is pregnant. Even on its own terms, the story doesn’t make much sense. It is rather as if Death of a Salesman had been crossed with Into the Woods – and the two don’t mix. On one level, the show is about a son’s belated recognition that there was hidden virtue in his bombastic tale-spinning father. But, since that realisation depends on accepting there was a grain of truth in the father’s lies, the show ends up having a nervous, each-way bet on fact and fantasy.

As in the movie, but unlike on Broadway, this version splits the role of Edward into his bedridden and storybook selves. Grammer plays the former with great elan and makes something almost endearing out of this grown-up Alabama Billy Liar. He tells us that “our town was so small our phone book was the Yellow Page”, and radiates the bonhomie of a man who lives in his dreams and cannot see a lily without wishing to gild it. But much of the narrative is handed over to his younger fabulating self, rather doggedly played by Jamie Muscato. Although there is lively support from Dean Nolan as a gentle giant and Forbes Masson as a boisterous showman, the women in the story are marginalised and Matthew Seadon-Young struggles to excite our interest in Edward’s son.

Nigel Harman’s production has shrewdly abandoned the spectacle that supposedly stifled the Broadway version and presents us with more homespun magic arising, in Tom Rogers’s design, from a hospital bedroom setting. But in a musical one looks for memorable songs and Lippa’s score falls sadly short. There’s a cheery wartime number, Red, White and True, with just a hint of the Andrews Sisters, and I was touched by Clare Burt’s rendering, as Edward’s wife, of a song signalling her marital devotion. Otherwise there is little to lodge in the mind in a middling musical that fails to exploit, in the manner of Follies, Edward’s split selves, and that doesn’t give us nearly enough Grammer.

• At the Other Palace, London, until 31 December. Box office: 0844-264 2140.