It's one of the most dangerous places in the world, but writer Adam Brace nevertheless takes us headlong into the heart of the Democratic Republic of Congo in his new play. The piece goes from London to the Congo and back again in the journey of hapless government stooge Stef, who has been tasked with putting on a festival to raise awareness of the plight of the country.

But though, in the awful bureaucracy and middle-management-speak, she is similar to characters in the TV comedy show Twenty Twelve, Stef isn't just a vessel for arch one-liners. She's witnessed the atrocities that happen in the Congo first-hand and it's the trauma from that experience which drives her. Behind her white, middle-class, privileged, government-savvy veneer, she literally can't face the idea that she has no power to help. Brace shows us a person desperately trying to do something - anything. But she comes up against a vast mountain of political conflict which includes a long history of abuse and terror. And it's not something one person can fix.

Brace's play is a complex, at times a little messy, multi-layered thing that never deals with the subjects of good-intentions or the Congo itself, lightly. But there are plenty of laughs, often at the pure ridiculous nature of some of the issues Stef faces – including finding an appropriate comedian/band/photographer and the impossible-to-unite festival committee (made up of figures from the Congolese community and British NGOs). Within the gags, Brace makes sure we learn a hell of a lot about the country itself and the current issues it faces: from the country's main mining resource - Coltan - which is used in our phones, screens and tablets, to the use of rape as a weapon in the civil war. Though all this information could feel token, it doesn't. Instead it is an important part of They Drink It in the Congo: Brace forces us to know more.

Michael Longhurst's in-the-round production keeps the pace up and has an exceptionally hard-to-watch central section where Jon Bausor's designs take on a new level – literally. It's this part that is the pivot for the two sides of the play, as we see what Stef experienced when she was working out there. It re-sets our view of everything else that plays out around it. In the second half, with a live band onstage, all screens turn into deformed palettes with nails protruding out of them. They are reminders of every individual's part in the Congo's problems. Accompanying Stef onstage throughout is a Congolese man in a bright pink suit. He's a kind of conscience figure, and though in the first half feels oddly superfluous, after watching what happens to Stef in the Congo, he is brought much more sharply into focus.

There's a superb ensemble cast who switch between the many characters and from British to Congolese (with surtitles) as needed. Fiona Button gives a very strong performance as Stef, and lets all the horror of her experiences, as well as her underlying guilt and shame, slowly bubble up to a climax. They Drink It in the Congo is a sharply funny look at charity in this country, but it also, most vitally, sheds light on one of the most shocking conflicts of our time.

They Drink It in the Congo runs at the Almeida Theatre until 1 October.