On the left of the stage, a screen projects the Miltonic line: “No light, but rather darkness visible.” On the right, a mother and son board a minibus to begin a treacherous journey out of their Ugandan homeland in 1979, as the nation is torn apart by political turmoil in the dying days of Idi Amin’s regime.

The boy is the play’s writer, the poet Nick Makoha, and this imaginative enactment of his escape out of Africa is a personal narrative about the loss of home, as well as a fractured story of a country as it descends into violent chaos.

Michael Balogun appears as both the grownup Makoha, sitting on the sidelines of the stage like an observer of his past, and as his younger self who boards the bus that will take him across the border to Kenya and beyond to Britain. The locus of the drama is the battered minibus, or matatu in Swahili.

Balogun and Akiya Henry play its numerous passengers, from Makoha’s mother to a pregnant woman, an English traveller and a political dissident, along with other characters such as checkpoint guards, street-sellers, soldiers.

The two actors make quickfire switches between characters and have a delightful synergy, but their individual traits are exaggerated to distinguish between them, and it becomes hard to keep up with the morphing voices, scenarios and time frames. In the end, this fluidity feels vertiginous and the drama scattered. While Roy Alexander Weise’s direction gives the play a collective sense of danger, there is less sustained emotional drama around individual lives and circumstances.

The staging is more successful. Rajha Shakiry’s set has a sense of perpetual movement, which conjures Makoha’s journey. It is formed of rows of seats on a bus and a bag compartment swaying overhead, but these are rearranged by actors to become a settee in a living room, then quickly, back into the bus.

The final scene, as Makoha’s traumatic journey ends with his arrival at Heathrow, is a shocking one. We do not see or hear him, and the focus is a slyly jeering immigration official: “I wonder how you got to Nairobi without a passport. On a matatu? Is that a fruit?”

The silenced Makoha becomes every child refugee who has witnessed horrors and struggled out of violence to encounter suspicion and disbelief in a country of refuge. In this moment, we see how Makoha’s drama is not just a piece of personal or Ugandan history, but very much a story of our times.

• Touring the UK until 16 February