Beryl (Rose Theatre, Kingston)

If, like many people, you'd have difficulty identifying the great names of 20th century women's cycling, you're unlikely to be familiar with the life and career of Yorkshire woman Beryl Burton, OBE.

As a sickly child who spent months in hospital after an attack of rheumatic fever in 1948 that left her with a heart condition, Beryl was told she should never undertake vigorous exercise again.

She ignored the advice, and trained ferociously hard with her local cycling club, eventually achieving astounding national and international success in a racing career that lasted almost 30 years.

So Maxine Peake's play – which began life as a radio play – sets about correcting the subsequent neglect of Beryl's legacy as a sportswoman and inspirational cyclist. And in these times of sponsorship and undreamed-of wealth that accompanies top sporting stars, it's salutary to realise that Burton was so out of pocket despite her victories that she also worked on a rhubarb farm to make ends meet. And even more astonishing to discover that she cycled from Yorkshire to London to take part in a race, as the train fare was beyond her means.

Director Rebecca Gatward skillfully creates an engaging performance that mingles the deceptive simplicity of Peake's narrative writing with a make-do-and-mend approach to the mechanics of the production.

One of its greatest successes is Mic Pool's real-time video projections, which allow us to follow Beryl through the glorious countryside she trained in. Pool is also sound designer and has clearly enjoyed gathering cycling (or at least bell-related) tracks from Kraftwerk, Queen and others, to punctuate the show.

Naomi Dawson's cycle-shed design manages to create intimacy within a huge space, and she also has fun with her knitting needles, creating one of the outlandish jumpers Beryl knitted to help her relax.

Samantha Power delivers a stirring performance as Beryl, both in and out of the saddle. Burton demonstrated a steely determination not to be kept down either by other people's low expectations, or her own heath problems, and Power harnesses all the ambition, energy and sheer grit shown by Beryl throughout her career – not least by cycling a good 10k during every show.

Beryl Burton's success was further fuelled by the support of her husband Charlie, played here with great good humour by Lee Toomes, who has become extremely adept at making it look as though he's chasing a racing bike that's actually static.

Rebecca Ryan is charming as the young Beryl, and also plays her daughter Denise, herself a successful cyclist. Dominic Gately is Nim, and takes on a number of female roles – including the Queen – with relish.

The play was commissioned and first performed by the West Yorkshire Playhouse in 2014, and its reach is now spreading beyond Beryl's home turf. She was clearly a legend, and Maxine Peake's play successfully puts Beryl Burton on the sporting pedestal where she belongs.

Beryl runs at the Rose Theatre Kingston until 19 March.