The Royal Court doesn't often revisit its past. As a new writing theatre, it lives in the present. Reviving Jim Cartwright's Road, which premiered here in 1986, is not just a six-gun salute to one of its own. It is a political act – a way of reflecting Britain back at itself and its past. Too little, you realise, has changed. For all its vintage trappings – big eighties hair and big eighties tunes – Cartwright's run-down industrial town looks horribly familiar. So much for the Northern Powerhouse.

Road leads us through a typical Lancastrian town on a typical Saturday night in 1986, Margaret Thatcher's Britain. It sweeps from dusk until dawn; a whole town drinking its worries away for a short while. Young men and women step out in search of a sup and a shag. Alcoholics scrabble a few quid for a can. Chippies hawk their wares come closing time: chips, chips and more chips. Scullery, a charismatic shambles, who may or may not be homeless, is our guide: Lemn Sissay plays him with a glint in his eye and a quart of rum in his hand. The road comes to noisy life in John Tiffany's revival.

It has a quieter side too though. Others stay at home, stewing over their lot, and Chloe Lamford's design delivers them onstage in a glass box – part prison, part display case – that rises up through the floor. Liz White plays a mother waiting up all night for an absent husband; Mark Hadfield, a middle-aged man pining for a gentler past. It's a tale of two towns, really: best of times, worst of times. The brash public face, dressed up to the nines, masks a different mood underneath: desolate, angry and very often alone. The vulnerable go unseen. They don't leave the house.

Road reflects the hardships of Britain's industrial decline, but it's much more than a ‘grim up north' play. Tiffany and Lamford tease out the play's patterns and motifs. Road reflects a massive crisis of masculinity: soldiers drink themselves semi-conscious, skinheads rage and rampage, while women – almost all of them – seek someone to hold them, often to little avail. It splits between young and old, too, as if Britain were both reinventing and forgetting itself at the same time.

First time around, Road was staged in promenade. Jane Horrocks scrawled graffiti on the Royal Court's front steps. The theatre's bouji bar was rebuilt as a traditional pub complete with dartboard and glitter ribbons. Ian Dury's Scullery led audiences into the lives and living rooms of Cartwright's Lancastrians. We were invited in. We witnessed a way of life. "You don't watch Road," one critic wrote at the time, "You live in it."

That would be preposterous today – nothing less than poverty tourism – and, in returning Road to the stage, Tiffany restores its theatricality. Rather than people, we see characters; scenes, instead of slices of life. Some even seem like Samuel Beckett shorts: June Watson's dementia sufferer dolls herself up at her kitchen table; Shane Zaza's Joey, unemployed at 26, takes to bed to starve himself to death, babbling as hunger turns to delirium. "Fucking long life, innit?" becomes a constant refrain.

Language, in particular, comes to the fore: a robust, instinctive poetry runs throughout Road. Sissay's Scullery dances a soaring pas-de-deux with a shopping trolley to Swan Lake – a wordless act of imagination that reflects the loneliness and materialism latent in Thatcherism. The final scene, too, justifies the revival all by itself, as four twentysomethings stick on Otis Redding and launch into flowing, uncensored beat poems full of hopes and dreams, fears and furies.

That's what you take away – particularly at a moment when today's playwrights have struggled to put austerity onstage, wrestling with the ethics and aesthetics of poverty. Cartwright empowers through eloquence and Tiffany raises people up and gives them a platform. For today's dramatists, Road offers a road map. It's far more than a trip down memory lane.

Road runs at the Royal Court until 9 September.