Muhammad Ali's biggest fight – for justice – comes to life in style

"Nobody sings Dylan like Dylan" was how the record company's slogan put it back in the 1960s. Equally, nobody plays Ali like Ali, then or now. So it was sensible of the director Stephen Frears and the screenwriter Shawn Slovo to mix original newsreel footage with newly shot material when putting together their film Muhammad Ali's Greatest Fight, which they presented to an audience at the British Film Institute on Tuesday night.

Its US premiere took place 24 hours later in Louisville, Kentucky, Ali's home town, kicking off Three Days of Greatness, a gala at which humanitarian awards were presented in the boxer's name to recipients including Jimmy Carter and Christina Aguilera. No one who saw it on either side of the Atlantic this week could doubt that if any sceptic, at any time in the future, were to question the wider significance of Ali's life, this film would at least start the job of putting them straight.

In this telling, Ali's greatest fight was not the Rumble in the Jungle or theThriller in Manila. Based on accounts in a book of the same name written a dozen years ago by Howard Bingham, the magazine photographer who became Ali's close friend, the film focuses on the events surrounding the US Supreme Court's decision in 1971 not to send the boxer to jail for his refusal to be drafted into the services during the Vietnam war. It was a moment at which the civil rights and anti-war struggles intersected, giving vital publicity and impetus to protests aimed at persuading the US government to extract its armed forces – with their disproportionate number of black servicemen – from south-east Asia.

Slovo told the London audience that, since Supreme Court deliberations are not minuted or otherwise recorded, it had been necessary to invent the exchanges leading up to the historic verdict by a group of judges whose average at the time was north of 70. She relied on the known histories of the nine men, who are played by a group of distinguished actors, led by Christopher Plummer, Frank Langella and Danny Glover.

"There's a kind of freedom in that lack of documentation," Slovo said, and if that is true, then she has used the freedom effectively to depict a body created to be free from political influence and yet whose chief justice, Warren Burger (played by Langella), was clearly operating according to the wishes of President Nixon.

For dramatic purposes, the screenwriter also created a group of younger lawyers attached to the individual justices, among whom the debate rages most fiercely. The most significant of them – the one whose commitment tips the balance – is played by Benjamin Walker, a 31-year-old American actor who was also present on Tuesday, telling the audience that, although he had boxed as a youth, he had been unaware of the details or the significance of the story with which the film deals.

"This was a time," Walker added, rather wistfully, "when young people were more involved in politics than I imagine they are today." You can say that again. And among the figures who inspired the young people of half a century ago was a boxer who, in Walker's words, "had the ability to remain composed and articulate in the face of a massive amount of opposition".

Frears, who so successfully cast Helen Mirren as the Queen and is currently making a film about Lance Armstrong with Ben Foster in the lead role, expressed his relief at not having to find an actor to play Ali. By using the newsreel footage to tell the story of Ali's rise, his conversion to Islam and his confrontation with the authorities, he injects immediacy and momentum to the narrative that unfolds within the Supreme Court building.

To boxing fans, Ali's legal battle perhaps took second place to his achievements in the ring. But Frears pointed out that, even after winning his world title back against George Foreman in Zaire in 1974, Ali was still enraged by the memory of the years stolen from him by the political establishment.

Cinemas no longer offer double bills, but I was fortunate to walk into Muhammad Ali's Greatest Fight straight from seeing Nothing But a Man, a 1964 film by the director Michael Roemer, little seen at the time but now restored and being shown at the BFI. Set in Birmingham, Alabama just before the civil rights movement broke surface, it deals with a young black man whose attempt to settle down and live a decent life is disrupted when he is sacked for attempting to unionise his co-workers at a sawmill and finds himself suddenly being turned away by other potential employers.

Shot in black and white, in the style of Italian neo-realist cinema, it captures the texture of life among men whose pride is destroyed by socio-economic powerlessness and women who have to cope with the consequences. Music – whether the gospel choir in a Baptist church or the sound of Martha and the Vandellas throbbing from jukeboxes, car windows and back doors – is everywhere.

Roemer and Robert M Young, his collaborator on the screenplay, end the film on a note of optimism, with the young couple at the centre of the film, played by Ivan Dixon and the great jazz singer Abbey Lincoln, repairing their relationship and resolving not to buckle under the pressures imposed by a racist society. But the modern viewer is aware that, between the making of the film and its release, a group of white supremacists dynamited a Birmingham church, killing four schoolgirls in one of the most terrible atrocities of the civil rights era.

That was how the world was when Cassius Clay encountered Elijah Muhammad, Malcolm X and the Nation of Islam, changed his name to Muhammad Ali, and forced the whole world, from boxing promoters to the president of the United States, to deal with the meaning of his gesture.

"You see him fighting for his principles," said Attallah Shabazz, Malcolm X's daughter, after seeing the film in Louisville, with Ali and his wife, Lonnie, also in the audience. Those principles continue to make him a worldwide symbol of resistance to oppression and discrimination.

Muhammad Ali's Greatest Fight was funded by HBO, which will broadcast it in the US on Saturday night, to be followed on Wednesday by a UK screening on Sky Atlantic. Nothing But a Man has just begun a run at the BFI. It was my luck to see the two films on the same evening, which is something that might never happen again – although it should, and not just by coincidence.