You'd have to have a heart dry as an old sunflower seed not to moved by Gary Barlow and Tim Firth's musical version of The Calendar Girls. Based on the – by now very familiar – story of a Yorkshire WI group who posed for a nude calendar to raise money after the husband of one of their members, Annie, died of cancer, the musical follows the hit film and play of the story (both also by Firth). But it proves a tale that still has the capacity to raise a smile – as well as funds for Bloodwise, a cancer charity.

It's a cosy affair, with a pleasing score from Barlow, but not without flaws. Structurally, the show is lop-sided: they don't hit on the calendar idea until the interval, giving the first half the slight feel of treading water, even if it does let us get to know the dying man who plants sunflowers "because they always find the light". But attempts to introduce conflict – a teenage boy is embarrassed by his mother's escapades and goes "off the rails" – are feeble: he's a head boy who's only fault is to pal sexlessly up with a sullen new girl and neck a couple of WKDs. As rebellions go, it's about as shocking as using cherries instead of sultanas in the scone baking competition. Ben Hunter brings more charm to the role than it deserves.

For a long while, it also feels like you could be watching Brexit Britain: The Musical, with bursts of "Jerusalem" and village fetes, everyone eating chips and drinking tea. England's "green and pleasant land" is created through banks of painted cupboards. Even the sodding clouds are of bunting. There's a background hum of some pretty retro sexual politics, too: a joke about a busty middle-aged woman "grooming" a teenager wouldn't be played for laughs if the genders were reversed, there's a pun-tastic song about plastic surgery, and the fact that these brilliant mature performers are referred to throughout as "girls" just rankles, frankly.

Oh, but all this gets swept away in a tide of good will, really. The pace picks up in the much better second half, and the calendar shoot, iced buns strategically in place, is both very funny and utterly cheering. These girls – no, women – are wonderful; not a dud note. It still feels rare and richly rewarding to see a musical with an older ensemble, and a 40-year friendship between Annie and Chris, especially, is beautifully brought to life by Joanna Riding and Claire Moore.

The score is predictably piano-led, although it also often swells with the plangent sound of a brass band (the whole thing is constantly underlined as Very Yorkshire). But Firth and Barlow deserve credit for their light touch with the sadder elements of the story. It would have been easy to make this desperately mawkish, but the portrait of grief is finely wrought, especially with Riding's sensitive performance.

The hummable "Scarborough" sees Annie contemplating her husband's death by wondering who'll help her change the duvet covers. In ‘Kilimanjaro', it's climbing the stairs to bed alone that's a real challenge, not a charity hike up a mountain. If lyrics occasionally strain too hard to be salt-of-the-earth – featuring squabbles over margarine in Tesco – for the most part, the music marries effectively to the everyday cadences and quotidian details of ordinary lives.

You probably know before reading a review whether a Barlow Brit-flick musical will be your cup of tea or not. And for a show that tries to present these women as unconventional, this is a deeply conventional show. Yet The Girls also blossoms into a feel-good hit as bright as a field of sunflowers. Sometimes, we need to turn towards the light.

The Girls runs at the Phoenix Theatre until 22 April.

Click here to buy tickets for The Girls