Williams stars as Raymond (Ray) Joshua, a street poet and petty drug dealer, whose flight from a gang-shooting with a quarter of a pound of marijuana in his pocket plunges him from the frying pan of the United States' capital's housing projects to the hellfire of its criminal justice system. The title puns on "the slammer" and "slamming" - the electrifying performance-poetry contests sweeping across America that hint at Ray's salvation.
The first fiction feature by the accomplished documentary film-maker Marc Levin, the story was inspired by Williams's winning performance in the annual grand slam at New York's Nuyorican Cafe in 1996. By the time the actor went to audition, "they had footage of me performing across the country - like I'd been stalked", he laughs. Williams, who wrote all Ray's poetry (but for a freestyle duet with a real prisoner in the neighbouring cell - "17 years old and serving 75 to life") sees the "underground poetry scene" as heir to hip-hop, the vibrant African-American street culture whose audience it often shares.
But its influences are wider. "I'm not a hip-hop poet," he says firmly. "Hip-hop is a rhythmic derivative of poetry. Whereas spoken-word, slam poetry, performance poetry, is poetry in the traditional sense - paying attention to metre, stanza. Most of us were raised on hip-hop and lyricism. But if hip-hop is the child of poetry, after a while you think, wow, I'd like to meet your parents - likeWalt Whitman and Shakespeare."
Through Slam's realism Williams is also hoping to debunk the pseudo-glamour of gangsta rap. Shot in nine days - seven in the prison - the film used real prisoners and guards. Williams's first impression was of a slaveship. "People asked, 'did you screen out the white prisoners?' No: there are no white prisoners in DC jail, despite the corrupt politicians and their often delinquent kids." He adds: "The first three days were the most depressing - there was no poetry in those grey walls. I see reciting poems as incantations, spells; they affect you whether you realise it or not. I've read in museums, churches, and loved the way it vibrated. But in prison there was no acoustic vibration; it was like still water. You could lose your voice trying to project in that place - which is a hell of a metaphor."
Still only 26, Williams admits the film's success has been slightly overwhelming. "You're put in a position to figurehead this thing, and it changes your life," he says.
Scornful of many of the offers now flooding his way, he says: "A film gets popular in festivals, and Hollywood says, 'Great: here's money to play another drug dealer'. Like, wow, I get to play next to Whoopi Goldberg, or whatever. It's bullshit. And the point of this film was to combat the bullshit".
He remains hopeful, however, convinced that Slam will plant "little seeds". "When a rapper like Coolio gets on national television after seeing Slam and says, 'yo, I saw this film and I wanted to recite a poem' - if we can get just two rappers not to play a part in the fucked-up programming of young people's mind-states - then those are the little seeds."