Selma is the latest in a series of recent films dealing with America's appalling history of slavery and civil rights, including Lincoln, The Butler and 12 Years A Slave.

Sooner or later this contemporary reappraisal had to reach Martin Luther King Jr.

This new interest has also reached the theatre. Last year on Broadway, All The Way dealt with Lyndon Johnson's successful efforts to pass the Civil Rights Act of 1964. The play was Johnson's story (with Bryan Cranston giving a barnstorming performance), but the key supporting character was King, sniping at the president's heels.

Ava DuVernay's film takes up the story in 1965 and flips the focus: this time King is at the centre of a defining moment in the civil rights movement. Despite black Americans ostensibly having the vote, dirty tricks employed by election registrars in the South continue to thwart them. Fresh from accepting the Nobel Peace Prize, Dr King (David Oyelowo) takes his team to Selma, Alabama, to campaign for "unencumbered voting".

Their plan is to demonstrate peaceably for voting rights, knowing that the bigoted local sheriff will respond with violence - hopefully on television - bringing the issue to national attention. And this is exactly what happens. With Alabama governor George Wallace (Tim Roth) also sending state troopers against the marchers, the outrage adds fuel to King's showdown with Johnson (Tom Wilkinson) in the White House.

The principal achievement of DuVernay, writer Paul Webb and Oyelowo is to make the saintly figure of King flesh and blood. The good pastor may espouse non-violence on his side of the fence, but he's prepared for the violence of others to win him an advantage, a provocation that takes him into a moral grey zone; the film also alludes to his marital infidelity.

At the same time we see a genuine team player, whose compassion in private moments is as stirring as when it's expressed in his famous speeches. If anything, the warts-and-all presentation makes him even more inspiring.

The plot is structured around the three campaign marches from Selma to Montgomery, each ending differently. DuVernay doesn't hold back when depicting the brutality against the marchers - though not gratuitous, these sequences are not for the squeamish. Behind the scenes the campaigners argue over tactics, King and Johnson lock horns over the President's decision to distance himself from the fray, and Wallace talks dirty tricks with his venal Southern acolytes.

There's also room for a cameo by FBI chief J Edgar Hoover (who informs the President that King is a "degenerate" who he's placed under 24-hour surveillance) and by Malcolm X. The result is gripping, shocking, often extremely moving. It's littered with good performances, from Roth's lizard-like Wallace, to Carmen Ejogo's dignified Coretta Scott King and Oprah Winfrey as Selma activist Annie Lee Cooper. But the eye of the storm is held brilliantly by Oyelowo.

Still best known here for his TV turn in Spooks, the Brit has had a busy but underwhelming career in America, often playing smooth baddies; maybe he was saving himself for this. Physically he's filled out for the role and added a deep timbre to his voice, yet there's nothing showy about the performance. His King is sombre, affected by the injustices around him, at times uncertain, but also a powerful and pugnacious presence. Examples of the famous oratory are sensibly few; when they do occur they resonate deep in one's gut.

There's never any doubt that Oyelowo's King means business. "As good a place as any to die," he says of Selma when he arrives. Fate had a different location in mind, in nearby Memphis, just a few years after this seminal victory.