Matilda the Musical, or, I loved it, almost without reservoirs.

Those of you who follow the London theatre news will have noticed that Sir Tim and the Lord have been complaining about the state of affairs for new musicals. This on the back of the early closing of their new shows From Here to Eternity and Stephen Ward the Musical. Sir Tim was quoted, I seem to recall, as complaining that there didn't seem to be a place in London for much apart from the jukebox musical. I can only assume that he hasn't seen Matilda, a show which definitively proves there is a place in London's West End for the non-jukebox musical, it just needs to be really good.

Obviously, I'm coming late to the party on this, but this is a simply wonderful show and I really hope that Tim Minchin (music and lyrics) and Dennis Kelly (book) will collaborate on something else. Like other recent musical theatre it is aware of the form's past. Miss Honey's moving Pathetic has a Sondheimesque wistfulness, the big musical number (possibly the Act One finale) when the light bulbs flicker round the blackboard echoes upteen similar finales, and Revolting Children was the best rock and roll pastiche I've seen for ages. But unlike so many other recent shows Matilda is enriched by this heritage, not buried. This show also succeeds in telling a good story (if I was going to be hyper critical it could be argued that there is a slight loss of focus in the second half, but the numbers are so compelling it doesn't matter) and being interested in its characters – two things, as regular readers will know, which I think essential to great theatre.

It was also instructive to see this show comparatively soon after seeing the National's Emil and the Detectives. Matilda stands out in contrast first, because it proves (Emil suggested far otherwise) that children can carry a show, but further the extraordinary thing is that most of the time you forget that many of the principal performers are children. Their choreographic precision, the quality of the characterisations, their flawless delivery of lines and songs is frankly incredible (diction is the only thing that sometimes falls a little short). Elisa Blake's Matilda is unfortunately the only such performer directly identified in the foyer, but at the very least Lavender and Bruce also deserve to be – whichever of the six Bruce's and three Lavender's was on they both deserve the very highest praise – Bruce knocked Revolting Children out of the park, Lavender's turn at the top of Act Two was hilarious. Blake meanwhile successfully holds the moving centre of the show.

The adult performers are also of a very high standard. Alex Gaumond is a suitably appalling Miss Trunchball with a perfect comic grasp of just the right tone of voice and moment for delivery. Haley Flaherty's Miss Honey is touching. I was especially delighted to discover Kay Murphy was playing Mrs Wormwood. I've been a fan of Murphy's since her outstanding Delores in the memorable Chichester Babes in Arms and she doesn't disappoint. The use of the Wormwoods is a nice instance of what good writers can do with what are in essence secondary characters, without disturbing the balance of the narrative. Mr Wormwood's (James Clyde) second act opening mangles words magnificently (this will – if you get to the show – hopefully explain the title of this review to you) and is followed by Telly where Michael (Joshua Wyatt) cleverly enlivens matters by dexterously catching a succession of books in a dustbin, and shouting at appropriate moments. Murphy, as on other occasions, draws the eye when she's on stage, and in partnership with her dance partner Rudolfo also has a number to shine in. The only weaker link is Mrs Phelps the librarian, although as the understudy was in yesterday afternoon this may be unfair – however I found the character a bit of a disturbing Caribbean stereotype which jarred with the rest of the show.

The production as a whole is wonderfully inventive, from desks to swings, to P.E. lesson. The use of letters and books as a motif is spot on. Peter Darling's choreography has an inventiveness comparable to Stephen Mear. The show as a whole is fairly mobile, but doesn't lose sight of the importance of those still moments between characters. Matthew Warchus and his associate directors deserve enormous credit. The band under musical director Laurie Perkins play with precision and sparkle throughout.

The show does have its poignant moments. Perhaps nowhere more so than in the juxtaposition between Matilda's forceful determination to fight back against wrong, and Miss Honey's grown-up timidity in face of same. How many of us, I wonder, have stood outside an office door as adults feeling we should go in and protest and turned and walked away.

But in the end this is a show suffused with joy. Everyone on stage is clearly having an absolute whale of a time, and the atmosphere is infectious. This is a show not to be missed.