The Children starts with a sunset: a glorious tangerine glow. It's like the day ends with a fanfare. Life too, so people say – one's sunset years. Lucy Kirkwood's latest, her first since Chimerica, throws a big old spanner in the works and puts the thumbscrews on the baby boomers. 'You made this mess,' she seems to say. 'You clear it up.'

As at Fukushima, a natural disaster has triggered a nuclear one. On the east coast of England, a power plant has gone down, reactors blaring. Various restrictions are still in play: scheduled blackouts and an exclusion zone. Hazel and Robin – retired nuclear scientists – live in an old cottage on its edge. Their dairy farm sits inside it. Its cows survived, miraculously, but their milk is undrinkable.

The Children begins with a blast from the past. Rose (Francesca Annis), a former colleague with a cool demanour, rocks up unannounced – so unannounced, Hazel near knocked her out in shock. They've not seen one another in 38 years, yet Rose – oddly – seems to know her way round the kitchen. Her return prompts an impromptu party – parsnip wine and reminiscing – but it drives to a singular dilemma. Rose is building a team to take over the clean-up from younger engineers. Will Hazel and Robin join her? Do they give up what's left of their lives for the sake of their children's generation?

It's two things at once: an allegory for climate change, and a portrait of the baby-boomer generation. Kirkwood's characters would live forever. At 67, Hazel's a yoga obsessive, saluting the sun (ironically) once a day, while Robin rides around the room on a kid's tricycle he's rescued, and drinks like a student. An earring glints from his left lobe. He's had both women on the go for decades – lived two lives for the price of one – and the unspoken love triangle leaves a malodorous atmosphere in the room. Rose, meanwhile, has accepted death. After a double mastectomy, she still smokes contentedly.

If there are lulls in the action, Kirkwood instils a fine mood – a heavy, melancholic languor – and speckles the play with moments of crack theatricality. When electricity kicks back in, she lets levity rush in with it. All it takes is a song to lift proceedings, and as the three oldies dance an old dance routine, you can see why they want to cling to life. The years fall off them, laughs bubble up and they seem, yes, sexy. Electricity makes us evergreen and pop culture renews itself. "I don't know how to live with less," cries Hazel.

This is, I suspect, a very different play to watch from different points in life: a clarion call for the young, a wake up call for our elders. Kirkwood suggests that a lack of responsibility is, ultimately, childish, but she's not unsympathetic. She recognises that children might make one more selfish, not less – parents being unable to stop mollycoddling their kids and desperate to see how their grandchildren turn out.

Designer Miriam Buether suspends the cottage kitchen in a deep void; a self-contained space surrounded by a blue-white glare. It's as if this one room had caused a solar eclipse; a planet all of its own, and James Macdonald directs with his customary meticulousness, fine-tuned to the moments when moods shift and silence hangs. It is a plaintive piece, heavy with fond memories and unspoken regrets – remote as Butterwoth, cruel as Pinter, but sad too; a deep-tissue sadness that can't be staved off with superficial pleasures and parsnip wine.

That's played beautifully by a brilliant cast. Each conveys a life lived – old aches, old hopes, old flames still burning. Deborah Findlay blusters as Hazel. She keeps busy, keeps up appearances, but for what? By the end she mulls another man like he were the biggest missed opportunity on the planet. Ron Cook, meanwhile, has the energy of an old rocker; his voice cracked after years on the tiles, still boogieing, still lusting. Annis glides around the space, sanguine and ethereal, as if she's seen through the fabric of the world and accepted its unreality. There's a lightness to her sadness, a freedom. She's ready to let go; ready to take responsibility.

The Children runs at the Royal Court until 14 January.