One of the best loved MGM musical movie classics - who doesn't want to make themselves a Merry Little Christmas, then? - is a real winter warmer at the Landor without positing a great case for the stage version which premiered on Broadway in 1989.

Vincente Minnelli's 1944 movie starred Judi Garland (soon to become his wife) as one of four sisters in St Louis getting over-excited and over-romantic on the eve of the World's Fair in 1904: hence the "clang clang clang" of the trolley song as they all jump on board in their straw boaters and crinolines.

Robert McWhir's perfectly sentimental production, with witty designs by Francisco Rodriguez-Weil (family portraits and front cloths, a good sense of social hoe-down) and notable musical direction by Michael Webborn (heading up a four-piece band at a slightly fuzzy keyboard) uses the authorised post-Broadway version.

This has a script by Hugh Wheeler, one of Sondheim's chief collaborators, all the movie songs, which are a mix of period favourites and newer items by Hugh Martin and Ralph Blane, and even a burst of "Auld Lang Syne". We start in high summer and end at snowy Christmas after grumpy old father (Bryan Kennedy), a lawyer, has rejected a summons to New York; St Louis is where it's at.

Impossible, of course, for sweet Georgia Permutt to get anywhere near Garland's incandescent pawkiness in the role of Esther, the most ebullient, and musical, of the daughters, but she sings the show's best song – "The Boy Next Door" – beautifully, charmingly duetting with Piers Bate's Princeton fresher whom she's targeted.

As in the Union Theatre musicals, a lot of the cast are straight out of drama school, and it shows; but there's eagerness and honesty in abundance. And when Robbie O'Reilly's choreography harnesses this exuberance in the trolley song, the "Skip to my Lou" square dance, or the society ball, where everyone is suddenly "doing" the banjo, the stage hums.

It also slightly ho-hums at the sight of Tom Murphy's Grandpa looking much sprightlier than the girls' father, or the splendidly voiced Carolyn Allen mixing up her spasmodically Oirish family maid with a village green biddy, or Thomas Judd's indecently tall suitor (of older sister Rose, beautifully done by Emily Jefferys) nearly bumping his head on the lighting grid.

But you wouldn't be going to see this at all if you didn't already love the movie, so the show becomes an indulgent wallow of shared happiness, ticking off the songs and renewing your memories of Judi Garland, or Mary Astor as her mother (Nova Skipp does look extraordinarily like her), or Maureen O'Brien as little Tootie. On second thoughts, I'll stick with the original.

Meet Me in St Louis continues at the Landor until 18 January