Guys and Dolls is certainly one of my all-time top five Broadway musicals – shaded in pole position by West Side Story? – and we've been spoilt for productions of this smart, witty and perfectly assembled New York fable by Richard Eyre (at the National in 1982 and 1996), Michael Grandage (for the Donmar at the Piccadilly in 2005) and now this enjoyable re-heat, with cast changes, of Gordon Greenberg's 2014 Chichester revival.

If you've never seen the show before, "More I Cannot Wish You," as the old Salvation Army stalwart sings to Sarah Brown. Straight-laced Sarah (Siubhan Harrison) is whisked off to Havana by high-rolling Sky Masterson (Jamie Parker) winning his bet against desperate Nathan Detroit (David Haig), who's trying to fix the floating dice game under pressure from the police, the other players and, most of all, his longstanding fiancée, the Hot Box dancer Miss Adelaide (Sophie Thompson).

Every strand of the smart and funny book by Jo Swerling and Abe Burrows, based on the stories and characters of hard-boiled scribe Damon Runyon, knits together in the salvation of the Salvation Army mission on 49th Street and the climactic show-stopper, "Sit Down, You're Rockin' the Boat," two encores neatly stitched in.

So, what's with the three stars? There's a lack of smack and relish in the discharge of the language, too much sloppy accentuation, and the sound system is dreadful, despite the best efforts of musical director Gareth Valentine and the lively band. Haig's Nathan, deftly done, is too nice and suburban, which is what he becomes, not how he should start. And brilliant Thompson, making Adelaide a lantern-jawed vamp with an over-used basso swoop in her voice, rather than a scheming, devoted sweetheart, swamps her precise, hilariously pointed numbers in production kerfuffle.

Whereas Julia McKenzie and Imelda Staunton built the cold itself into the "Lament" lyric, Thompson snuffs her sniffles in broader strokes, and "Take back your mink, take back your poils; what makes you think that I am one of those goils?" gets it laughs only in the surprise, haunch-handling striptease and the stand-in ermine draped round Valentine's neck in the pit. The musical finesse of Frank Loesser's wonderful songs is best served up in Parker's Sinatra-like crooning of the galvanic "Luck Be a Lady" and his clever ornamentation in "Sue Me" ("What can you do me?").

The crazy choreography of Carlos Acosta (no less) and Andrew White is a little cramped on this small stage, and Peter McKintosh's functional touring design (first stop, Liverpool Empire in March, then nationwide through July, as Parker re-adjusts to Harry Potter) is a slightly drab vortex, suggesting the crap game sewers from the off, fitted out with period advertising posters.

Overall, the show doesn't have the shimmer or the sassiness of the Eyre revival, nor the social grip and precision of Grandage's. But it still has the best musical theatre score in London, and a touching Laurel and Hardy double-act from Ian Hughes and Gavin Spokes as Benny Southstreet and Nicely-Nicely Johnson.

Guys and Dolls runs at the Savoy Theatre until March 12