Enoch Powell's own words sit at the centre of Chris Hannan's play. Ian McDiarmid stands in a spotlight and recreates the "Rivers of Blood" speech in full, pausing where Powell paused, stressing what he stressed. Around him, others look on: Powell's wife, beaming with pride; a white liberal friend, horrified; a Pakistani immigrant, expressionless; a young black girl, uncomprehending, and her future self, now an Oxford academic researching racial identity. All of them hear something different. All see a different man.

We look on too: a diverse audience almost exactly half a century on. To us, Powell's words are both familiar and not. Familiar, because we know of them; a speech distilled to a sentiment, even to a single sentence that, in predicting violence, seemed to incite it. "Like the Roman, I seem to see the River Tiber foaming with much blood." Familiar too, because we hear the same sentiments echoing around our own politics today: the breaking points, the wide-grinning ('watermelon smiling') "piccaninnies"; violence as "the next step."

Yet, Powell's words are unfamiliar too, rarely spoken in full; distorted by time and dismissed by history. Hannan restores their character and context: a minor Tory politician attempting to maximise his media coverage. On the advice of his friend, the liberal local journalist Clem Jones (George Costigan), Powell schedules the speech for a quiet Saturday afternoon and provides his own pull-quotes for lazy hacks. Hannan brings history back to life: a black and white photo recoloured. It sheds light on the present.

The theatre comes from seeing Powell made flesh. McDiarmid goes beyond impersonation to interpretation. He cuts a peculiar figure: pinched and pernickety in a patrician three-piece suit. His voice is repellent yet striking; thin but piercing. It seems to catch at the top of his throat, cracking like a pubescent chainsmoker's. Crisp precision slides into a lisp. You can't take your ears off him, that's the problem. (Nor can the press.) You tune in to the repugnant views of an arrogant aesthete who laments the loss of empire, who takes half a step back whenever an immigrant holds out a handshake, who reflects the public's ignorance back at them for his own political ends. He's the Ghost of Farage Past; the sneer beneath Nigel's jocular smile.

The surrounding stories buffer and balance out his views; a spectrum of racism and liberalism, both built on trad British values. We see the street of Powell's speech, its lone white woman, war widow Grace Hughes (Paula Wilcox), surrounded by new neighbours she can't understand. That she marries one of them, a bright Pakistani, might rebut Powell's words, but it co-opts her every bit as much as he did. (Druscilla Cotterill, allegedly, was more like Powell's portrayal than Hannan's.)

The play jumps forward too, to 1992, where Rebecca Scroggs' academic is retracing her childhood back to that street. She – one of Powell's piccaninnies – spat at her white neighbour. Racism, as her colleague suggests, comes in many colours.

Hannan's structure sets up eloquent and forceful head-to-heads, but in giving space to vital debates, each strand gives up its narrative drive. Identity, he argues, is an elusive, shadowy thing that shifts like the seasons. Fast-forward 25 years, and McDiarmid's Powell tremors with Parkinsons; a frail old man unable to control his body or his reputation, just as he was unable to control the course of history or the way his words were taken. "I was a storm," he says. "I was also a man entirely alone in a storm."

What Shadows runs at Birmingham Rep until 12 November.