First Night: Her Naked Skin, Olivier, National Theatre, London

This is the first new play by a living female dramatist to make it on to the epic Olivier stage in the National's history. A landmark moment, therefore, and symbolically apt that it has been achieved by a deeply affecting and rousing drama, by Rebecca Lenkiewicz, about the suffragette movement at its militant height before the First World War.

The play opens with archive footage of the cause's first martyr, Emily Davison throwing herself under the King's horse at the 1913 Derby. It shifts to a smoking room in the Commons where Asquith and cabinet colleagues are discussing damage limitation.

This sharply satiric episode shows what the women were up against. They are dismissed as "a lunatic fringe of lonely, frigid women who crave attention". One buffer suggests that, were Davison to survive, it would be a demonstration of "universal female incompetence". The solution is to distract the public with an artificial stirring up of the Home Rule question.

Skilfully balancing the wide-angled and the intimate, Her Naked Skin shows the struggle in its own right and as it impinges on the erotic affair between two suffragettes – a married toff, Lady Celia Cain (Lesley Manville), and a young seamstress, Eve Douglas (Jemima Rooper). They meet in Holloway.

The jail, here a monumental stack of cages, dominates Howard Davies' striking production, which forms part of the Travelex £10 season. We see the women smashing shop windows; at shooting practice in Epping Forest; harassed by protesters at a Hyde Park rally. And we see the reprisals of the establishment. A scene of the forcible feeding of a hunger striker – illegal and perilous – is as upsetting as the blinding of Gloucester in Lear.

Not that this even-handed play is unfair to men or blind to tensions in the movement. Imperious and complicated, Manville's brilliantly acted Lady Celia has grown out of her marriage to her childhood sweetheart. But she refuses to acknowledge that, after 15 years of supporting her in the cause, her husband is suffering from emotional neglect. By his own lights, he's trying to protect her from the damage of prison life when he presents her with the ultimatum of either stopping illegal activities or being exiled from the marital home.

The lesbian affair, achingly sad, comes to grief because the two women have different expectations shaped by social class. Lady Celia has a position to keep but an upper-crust casualness about clandestine flings. Rooper's haunting Eve is both less and more conventional in wanting monogamous commitment, albeit of a same-sex variety. Celia only realises what she has forfeited when it is too late and Manville's anguish is harrowing.

Susan Engel is superb as Florence Boorman, a blue-stocking campaigner of great spirit and fervour, if occasionally a little tough on human weakness. It's through her that the sometimes very funny script expresses its caustic wit. When a prison doctor complains that one of his colleagues was horse-whipped by some of her women, she retorts: "I hope he paid them the going rate."

It's humbling to be alerted to the courage and sacrifice of such forgotten women. This play is a salutary reminder for both sexes in our apathetic age that the hard-won vote can be seen as not just a democratic right but a democratic duty.