The ravenous, toothy croc in Roald Dahl and Quentin Blake’s 1978 picture book sparingly uses singsong phrases as he endeavours to procure a “child for lunch” whose “bones go crunch”. This musical version for over-fours finds the joy in abundant rhyme as two frogs share a log along the Nile, home of an “awful reptile”.

Lyricist Suhayla El-Bushra and composer Ahmed Abdullahi Gallab’s songs get off to a snappy start while Jessica Hung Han Yun’s lighting and Fly Davis’s set create a dense jungle that should complement Regent’s Park Open Air theatre where this show runs next summer. One inspired early scene finds a row of crocodiles at a dentist’s run by birds who use their beaks to extract the grisly bits of dinner between their clients’ gnashers, bringing to mind the leftovers lodged in Mr Twit’s beard.

That addition is pleasingly Dahlian but elsewhere Emily Lim’s production is often monotonous as it spreads this one-note story of a one-track croc across 55 minutes, adding a story of intrepid young campers and losing the fairground fun. El-Bushra’s script is sometimes flat and the thwarting of the beast’s tricks becomes samey in this staging.

Co-director Toby Olié’s splendid puppets, often integrated into Davis’s costumes, are operated by a lively cast of five. As the croc, Elliotte Williams-N’Dure has a crafty cackle and an often crazed look as she either wields his giant jaws or wheels around the stage on a striking, if occasionally cumbersome, croco-mobile that may end up on some kids’ Christmas lists. Charis Alexandra (Trunky the mild-mannered elephant), Lawrence Hodgson-Mullings (Humpy Rumpy the farty hippopotamus) and Robyn Sinclair (Muggle Wump the quicksilver monkey) join the others in some effective crowdwork with the audience, who are encouraged to mimic tree frogs and river hogs, and to pelt the stage with prop nuts.

Philippa Hogg’s exuberantly plumaged Roly Poly Bird stands out, although her cabaret-style entrance on a fringed swing needs a more distinctive accompaniment. The compositions (with additional music and lyrics by Tom Brady) often have an appealing brassy swagger but lack variety and there’s also some earnestness about teamwork and being brave. Here and there the show overcooks the story’s sly tone and measured darkness, especially in a jarringly triumphant ending. Amid the chants of “we got him! … come join the fun!” I felt rather sorry for poor old sizzled croc.

• At Leeds Playhouse until 6 January