This is one of the most disturbing evenings I have ever spent in a theatre. Stephen Emmott, an acclaimed scientist, stands in a re-creation of his cluttered Cambridge office and delivers, under Katie Mitchell's astute direction, an illustrated 60-minute talk on the consequences of over-population. He tells us that we are facing "an unprecedented planetary emergency" and, under his calm exterior, you sense a concealed fury at our failure to address the crisis.

Emmott uses an array of statistics to reinforce his argument that the current global population of seven billion will grow to 10 billion, maybe more, by the end of the century and that is unsustainable. We are facing a crisis with ecosystems being destroyed, the atmosphere polluted, temperatures rising and a billion people facing water shortage. "Things," Emmott sombrely reminds us, "will only get worse" as the demand for food doubles by 2050, climate change intensifies and the transport system that sustains our needs grows.

Describing himself as "a rational pessimist", Emmott says there are two solutions. We can "technologise" our way out of trouble, through building things like solar shields, or we can change our behaviour – by consuming "less food, less energy, less stuff". Emmott sees little chance of this happening. I think he is too scornful of energy-saving gestures. He tells us he's fed up with reading about celebrities giving up 4x4s in favour of an energy-saving car and says it's not going to affect the world's water supply if we wee in the shower rather than the loo. But at least every little helps.

Emmott is on surer ground when he castigates politicians and world leaders. "Thirty years of words and inaction," he predicts, "will be followed by another 30 years of words and inaction." As one of Emmott's many public roles is as scientific adviser to the Chancellor of Exchequer, I'd dearly love to know what happens when he tells George Osborne what he is telling 80 people a night in the Theatre Upstairs.

Some will argue this is a lecture, not theatre. But the distinction seems to me nonsensical. David Hare gave us his perception of Israel and Palestine in Via Dolorosa. London's Tricycle Theatre has staged edited versions of public inquiries such as those into the Metropolitan police's handling of the Stephen Lawrence case and Bloody Sunday. And the Finborough in Earl's Court is presenting The Fear of Breathing based on verbatim reports from inside Syria. Theatre is whatever we want to be and gains immeasurably from engaging with momentous political, social or scientific issues.

Overpopulation is too big a subject to be ignored and what is impressive is that Professor Emmott argues his case with an implacable logic. He is quiet, humane and deeply concerned and when he says, at the end, "I think we're fucked" you have to believe him.

Until 11 August. Box Office: 020 7565 5000