A collective gasp in a theatre is always a nice thing to be part of. But when it comes from a bunch of fidgety young children, it's something really special.

One came from the crowd while I watched Mr Popper's Penguins – which arrives in the West End following a UK tour. It marked the moment a wooden box in the centre of the stage came apart to reveal Captain Cook, an Antarctic penguin about to make himself at home in Mr Popper's front room. There he was, puppet penguin in all his glory, and the kids were absolutely delighted.

It's Nick Barnes' puppets which really tickle the little ones in Emma Earle's show. The two main penguins (Captain Cook and Greta) are no-frills – basically soft toys with handles – but they are supremely expressive in the hands of puppeteers Toby Manley and Lucy Grattan, whose bird squawks are both funny and realistic.

The show tells a story of a simple man and his wife. Mr Popper loves to dream of being an adventurer, but is satisfied as a painter and decorator and living with Mrs Popper in the quiet town of Stillwater. It's when he sends a letter to one of his heroes – Admiral Drake who is on a trek to the South Pole – that he gets sent a penguin. And then is sent another. The penguins disrupt the couple's lives in the best possible way, turning them from upright, everything-in-its-place people, to risk-takers and fun-makers. Eventually they end up heading out on the road with their penguin troupe. They train the penguins up to become a music hall act and perform in theatres across the land.

Earle's direction is slick and beautifully timed. The clipped dialogue and derring-do attitudes in the adaptation hark back to the time of the original book, which was first published in 1938. It's Zoe Squire's designs that also make the piece: they are uncomplicated, but regularly surprising. Ice is made from white sheets, and the havoc that the penguins wreak on the Poppers' house is ingeniously realised, with paint pots and big pieces of furniture – goldfish bowls and ornamental globes to name two - getting hurled about the place.

The songs are light and joyful, and sung very well by the excellent cast. The numbers are occasionally a little long and it was during these where I saw the really young ones near me struggle with concentration. But the moment the penguins get back to their naughtiness was the moment the audience were hooked back in.

This is high class storytelling with huge heart and some lovely surprises.

Mr Popper's Penguins runs at the Criterion Theatre until 31 December.

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