Around the world in 80 days? More like around the stage in 80 ways... American playwright Laura Eason's adaptation of Jules Verne's classic adventure story calls for lo-fi theatrical invention, and a robust sending-up of Victorian gents' indomitable spirit and staggering privilege. Lucy Bailey's production doesn't quite do enough of either, although the overall effect is still whimsically winning.

Phileas Fogg is the most exacting gentleman in England, obsessed with "mathematical precision" – so if it's technically possible to get around the world in 80 days, he'll jolly well do it. Fogg bets his fortune on his success, and goes off with a hardback book of international transport timetables and his valet, former circus performer and comedy French man Passepartout. Naturally, they soon get into all sorts of adventures: there are detectives to be thwarted, bandits to be seen off, women to be rescued, and love to be fallen into. It's a voyage of self-discovery – learning to see with new eyes – even if Fogg begins comically, imperialistically blind to the world.

Robert Portal is simply splendid casting as Phileas Fogg: he does stiff upper lip and clipped RP to a T. Tall and well-upholstered, upright and proper and yet sweetly awkward around his love interest Mrs Aouda (Shanaya Rafaat, heart-melting indeed). Simon Gregor plays his physical foil - short, spry, and capering - yet I found his clowning rarely hit the mark. You noticed him playing funny rather than yourself laughing; to be fair, Eason's script fails to provide much wit.

Django Bates' fast-changing music may not be subtle, but it helps whisk us from country to country, as do a hectically multi-tasking chorus who attack a selection box of accents with gusto, if not finesse. A particular mention must go to Tim Steed, who deadpans his way hilariously through a host of characters – until he fluffs a line and corpses most of the cast, which proves even funnier.

The ensemble seem to pop out all over the brilliant set – Anna Fleischle, who just won an Evening Standard award for Hangmen, provides the versatile and charming staging. A rackety wooden box is full of hatches and pullies; these are put to especially ingenious use at the start, to suggest Fogg's comfortable routines, with toast landing perfectly on plates and top hats appearing through floorboards. On their voyage, simple pieces of wooden furniture and sails are one minute an ocean liner, the next a sledge, the next – lovely this – an enormous elephant. Fleischle also makes visible the area below the deck, where coal must be shovelled to keeps those trains and ships moving.

There are flashes of delight and ingenuity here – but only flashes. Too often, one good idea is flogged rather than skipping on; too often, the pace sags like a sail without wind. And that subterranean level, making visible class divisions, feels underused: a concept there hasn't been enough time to explore.

It's all entertaining stuff - you're not going to have a bad time at this show – it's just that creatively-staged family entertainment, especially at this time of year, has a pretty high bar to leap over. Like the rest of the audience, I'm cheering for our intrepid travellers by the cockle-warming end of their epic journey, but it's not just about the destination, is it?

Around the World in 80 DaysAround the World in 80 Days is at the St James Theatre until 17 January