There are some good jokes in Peter Quilter’s new play and Maureen Lipman knows how to land them. “Some do cocaine, I do cabaret,” she shrugs as Allegra, whose singing is annoying her neighbours. “The ironic thing is it’s the cabaret that gets up people’s noses.”

Allegra’s spontaneous serenades – at the butcher’s, the bakery, the hairdresser – are increasingly unwelcome in her village. Waiters march her out of restaurants, and even the local choirs have banned her. Her brother Ronen (John Middleton), worried for her health, employs a Czech care worker to make sure she eats. Every now and then Lipman gets a twinkle in her eye, a shimmy in her shoulders, and launches into a tune.

And that’s about it, in a production by Stephen Mear that’s heavy on the whimsy and light on everything else. Allegra presents like one of Alan Bennett’s lovable, spirited eccentrics, but we learn nothing about her beyond her unworldliness. The stashing of her father’s ashes in a series of food tins – a setup for a joke that never quite pays off – is the closest we come to backstory.

If Lipman feels a tad quieter than is her wont, it may be because she’s having to build character on quirky costumes and fantasy-sequence lighting. The plot involves a brush with a barely recognisable justice system that wants to force Allegra to regulate her colourful mind with drugs. A police officer doggedly prosecutes a little old lady for performing Annie at a petrol station, and a judge court-orders medication for someone who poses no danger to themselves or anyone else.

Meanwhile Anna (Elizabeth Bower), an ideally compassionate care worker, fights her corner with the zeal of someone born under Soviet rule, who also happens to know obscure lyrics from the Great American Songbook. (Personally I love a rousing chorus of Take Me Out to the Ball Game – but if you’re trying to encourage audience participation, don’t pick a song completely alien to most Britons.)

Twenty years ago, Lipman starred in Quilter’s play Glorious! about Florence Foster Jenkins, the New York socialite deemed opera’s worst ever singer. There’s a clear through-line to Allegra, whose uninhibited happiness and unconventional way of expressing it is deemed inappropriate by society. “Given all the misery around … if you spend the day smiling, there must be something wrong with you,” says Ronen. It’s a fair point, but a shame that Quilter must hammer it home so hard.

• At Richmond theatre, London, until 13 June. Then touring until 4 July and at Harold Pinter theatre, London, from 8 July to 8 August.