Guys and Dolls, Savoy Theatre

The seemingly eternal British love affair with Guys and Dolls continues apace with the (somewhat recast) transfer to London of the Chichester production from two summers ago, and a more buoyant way to inaugurate the new theatrical year is hard to imagine.

Though built for touring, as is evident from the utilitarian feel of Peter McKintosh's fan-shaped design, Gordon Greenberg's staging in an instant brings necessary brio and dash to the West End, supplanting the psychologically anguished "musical fable" that was Gypsy at this same playhouse for most of last year with Frank Loesser and co's giddy "musical fable of Broadway". And just as Imelda Staunton's Momma Rose pretty much defined the musical theatre milieu during most of 2015, at least two of this production's four stars give performances to treasure, Jamie Parker in particular preceding his incipient fame as theatreland's Harry Potter with an absolute honey of a performance as the high-rolling Sky Masterson.

A regular in classics and new plays (The History Boys preeminently) who has segued to musicals big-time over the last year or two, Parker has never been in better, more insouciant command than as the silver-tongued Sky, the gambler whose sojourn to Havana with the evangelical "mission doll" Sarah Brown (Siubhan Harrison) finds this smoothie smitten against the odds. Bringing genuine Sinatra-style flair to the role played not by Sinatra but by Marlon Brando in the film, Parker is effortlessly winning, whether landing some lovely harmonies on "I've Never Been in Love Before" or surrendering to a love for Sarah that surprises no one as much as Sky (aka Obadiah) himself (Harrison and Parker pictured above).

And though her musical theatre chops have long been in evidence, not least via a pair of Sondheim revivals at the Donmar that resulted in nominations and awards, Sophie Thompson has an absolute field day as that "well-known fiancée Adelaide", the Hot Box chanteuse who has been trying for 14 years – and across multiple children invented to appease her mother – to bring her beloved Nathan Detroit (David Haig) to the altar. Playing down the sniffle-induced sounds that go with this role (she says "pearls", for instance, not "poils"), Thompson totters about in heels piecing together words like "respiratory" and "psychosomatic" as if she were learning some new language, when the tongue this character really speaks has to do with a voracious desire for domesticity that Thompson's devouring eyes and mouth make newly vivid.

Never the subtlest of performers, Thompson is theatrically and temperamentally at one with this role, and it's worth noting the skill with which she can shift from a full-throated embrace of Loesser's timeless score to admit, plaintively, to "the feeling she's getting too old" – this is an Adelaide alert to life's passing abrasions, so all the more reason that she have Haig's very sweet if none-too-ethnic Nathan alongside to take that journey with her.

Haig, in turn, deserves credit for not getting hung up on the accent of a part that has mired too many of its previous British interpreters in a surfeit of Runyonese. He may be a more ordinary-seeming Nathan than one is used to, but that's not necessarily a bad thing in a show featuring no shortage of eccentrically-named characters –Harry the Horse and the like. Throughout, one gets the feeling that Greenberg has encouraged his cast to invest in playing people first and their particular curlicues second.

With the exception of Harrison's wanly acted and sung Sarah (always a tough role: who ever wants to be the straight man - or woman?), the production is notably well served through the ranks. I can't recall a bigger Big Jule than the gleeful hulk that is Nic Greenshields, while Neil McCaul (pictured above) lends unusual pace as well as pathos to "More I Cannot Wish You", band member Arvide Abernathy's eloquently expressed bequest to his granddaughter Sarah that is arguably the most undervalued song in a score awash with standards: the second act, in particular, reels from one to the next. 

That act's celebrated showstopper, "Sit Down You're Rockin' the Boat," brings well-earned beads of sweat to the brow of Gavin Spokes's irresistible Nicely-Nicely Johnson, the choreography by Andrew Wright and Carlos Acosta allowing the ballet world's Acosta to honour his homeland as and when Sky whisks Sarah off for their Bacardi-spiked date in Havana. The dancing here isn't the defining feature of the production the way it was when Rob Ashford choreographed the same show for Michael Grandage a decade or so ago, but it's fun to see the cast in motion from the overture onwards, New York suggested more by its ever-zany denizens (a bicycling nun – or is he?) than by the somewhat generic feel of the design. 

Quite how Sky and Sarah managed during the five-hour flight to Cuba and back is among the multiple aspects of a Jo Swerling-Abe Burrows book that has always made a point of cutting to the chase. Amidst a near-perfect musical, "Marry the Man Today" here as ever feels as if it's missing the scene that might anchor the pell-mell nature of the finale. Still, Guys and Dolls has been slaying audiences since 1950, and with Parker on hand to croon his paean to "lady luck", I suspect it's the Savoy audience that will feel lucky over the next 10 weeks.

• Guys and Dolls at the Savoy Theatre until 12 March