Kelsey Grammer, star of the long-running sitcom Frasier, is definitely a star turn. With that great domed forehead, flyaway hair and a face that crumples with emotion, he can sing, dance a bit and hold a stage as effortlessly as he once held a screen.

He is the principal reason to see Big Fish, a musical based on Tim Burton's syrupy but heart-warming 2003 movie, which is tantalisingly close to being a really good show but somehow just fails to reel in its catch.

It has taken a long and winding road to the Other Palace. It has a book by John August, who also adapted Danny Wallace's original novel for the screen. Music and lyrics are by Andrew Lippa, whose impressive musical pedigree includes the Broadway hit The Addams Family. It is receiving its British premiere in a substantially reworked and reshaped version four years after its initial brief run on Broadway, in a production directed and choreographed by Susan Stroman.

There are many things to like about the result. The story, wherein retired travelling salesman Edward Bloom tries to resolve his troubled relationship with his son Will while lying on his hospital bed after suffering a stroke is tailor-made for musical treatment since it revolves around the tall tales Edward tells about his life. These include calming a giant and running away to join the circus – perfect inspirations for Lippa's joyous music. His songs may not be incredibly memorable, but they are both melodic and witty.

There's emotional depth too. Will is a journalist, his extreme rationality and search for the facts, sharply contrasted with his father's winning ability to spin fantastic stories. "You were born a tiny middle-aged man," Ed snaps, "Your rainbows are all shades of grey." As Will faces up to the challenge of his own impending fatherhood, the issue of what is true and what matters takes on increasing force.

Nigel Harman directs with panache, with designer Tom Rogers, lighting designer Bruno Poet and projection designer Duncan McLean transforming the tiny stage with flair and invention. The scene in the circus is energetic, funny and engaging. The moment when Ed imagines his hospital room transformed into a navy battleship is a feast of song and dance of which choreographer Liam Steel can be rightly proud.

The problems are all structural. The first act, in particular, seems to have too many songs of too many contrasting textures. The duet in which Will's wife and mother Sandra (lovely Clare Burt) sing of the challenges of parenthood is tender and touching but seems to belong to a different show than the sentimental "Daffodils", in which Ed and Sandra declare their love.

Furthermore, in reworking the show, the writers have decided to introduce a young Edward (in the shape of Jamie Muscato) which both crowds the stage with characters and their younger selves and pushes Grammer to the back of the action. He only really reappears to claim his central role in the stronger, more coherent second half.

Muscato is appealing and lively but it is not quite enough. He gets energetic support however from Forbes Masson doubling brilliantly as Edward's nemesis Don and as Amos, a ringmaster who turns into a werewolf (it's that kind of show) and Laura Baldwin as a charming young Sandra. As Will, Matthew Seadon-Young finds just the right mixture of up-tight resentment and winning charm, and Frances MacNamee is warmly winning as his wife Josephine.

But it is Grammer who glues the show together and you miss him when he is not there. He does all the things you'd expect of him – exhibiting charisma, charm, and superb comic timing. Then, just when you least expect it, his face dissolves, his voice cracks and he reduces you to tears. It is a five-star performance in a frustrating show.

Big Fish runs at The Other Palace until 31 December.