Thirty years ago, it was not uncommon to encounter white, middle-class suburban and provincial teenagers wearing badges that proclaimed "SMASH THE SPG". The primary spark for their opposition to the Metropolitan Police's Special Patrol Group and its role in policing London's immigrant communities came from the work of Linton Kwesi Johnson. When the SPG was eventually disbanded in 1986, it was under a deluge of public condemnation. It is not too outlandish to suggest that Johnson's poetry and music shaped that opinion: so much for Auden's claim that "poetry makes nothing happen".

Johnson's debut album, Dread Beat an' Blood, was released in 1978. It comprised poetry written in an uncompromising Jamaican-London vernacular and militant politics set to a reggae accompaniment. The combination ensured that his vivid and angry stories of Brixton street life and police brutality broke out of their south London setting to acquire a resonance far beyond location or race. Follow-up albums Forces of Victory (1979), Bass Culture (1980) and Making History (1983) provided the soundtrack to a remarkable period of postwar history during which the children of the Windrush generation of Caribbean immigrants established their permanent place in British society.

Tomorrow evening, Johnson performs at the Barbican as part of The Harder They Come, a season featuring stage and screen presentations of the classic Jamaican film of the same name. But the concert is also, in part, a celebration of the 30th anniversary of Dread Beat an' Blood, and might indicate something of an accommodation between the revolutionary poet and the British cultural establishment. In the years since Dread Beat an' Blood, Johnson has found himself one of only two living poets - the Polish Nobel laureate Czeslaw Milosz was the other - on the Penguin Classics list. Last year, Shakespeare expert Jonathan Bate presented a programme on Radio 4 acclaiming Johnson's poem "Di Great Insohreckshan", which responded to the 1981 Brixton riots - "It is noh mistri / we mekkin histri" .

But to see Johnson as a one-time radical turned national treasure is not quite accurate. Witness the Sun newspaper's distaste after his appearance on the Today programme last year, during which listeners were "subjected for nearly five minutes to the thoughts of the 'reggae poet', as his publishers call him, Linton Kwesi Johnson, whose most famous words are: 'England is a bitch.' Johnson came out with a rant about racism then proclaimed that, in his view, England was still 'a bitch'."

In any case, to focus on whether or not Johnson has earned the approval of either the political or cultural establishments is to miss the point. That they have taken note of him, he says, "is great. But they recognise me, not the other way round. Some black and Caribbean poets seek a kind of validation from these arbiters of British taste. But they really didn't exist for me. I was coming from a position of cultural autonomy. I did my own thing, built my own audience and established my own base. My audience was ordinary people."

Johnson was born in rural Jamaica in 1952 and was brought up by his grandmother after his parents separated. Their village had no streetlights, running water, radio, TV or newspapers, and he hardly ever saw a car. The hub of social life was the church, and his most memorable early reading was the Bible. "I would read the Old Testament and the Psalms to my grandmother, and that was my first introduction to written verse. People there know it, or at least bits of it, by heart. Illiterate people could quote from it and it was used in everyday conversation. You'd hear phrases like 'the hotter the battle, the sweeter the victory' all the time. At least half a dozen reggae songs use a variation on that line."

He left Jamaica aged 11, in 1963, to join his mother who had emigrated to London the year before. He experienced surprisingly little culture shock, but was taken aback by the "hostility to black people, particularly from my contemporaries at school. And also from some teachers who couldn't hide their contempt. There were also some very kind and good teachers, but a few were real bastards."

There was some exposure to literature at school - "I remember The Caucasian Chalk Circle and Under Milk Wood" - but it was via a sixth-form debating society that he encountered Althea Jones of the Black Panther movement, "perhaps the most remarkable woman I've ever met", which led him to attend Black Panther youth meetings. "She was a simply brilliant orator and a great teacher. That's where I got my real education. A whole new world opened itself to me and I started reading all kinds of stuff. It was the formative period of my life."

Under the influence of another political and cultural mentor, the publisher John La Rose, Johnson was introduced to African, Caribbean and American writers. "I discovered the Francophone poets such as Aimé Césaire and Léopold Senghor. I discovered Nicolás Guillén from Cuba and Pablo Neruda from Chile, as well as the likes of Jean-Paul Sartre and Hermann Hesse - hip authors of the early 70s. And I eventually discovered people such as Shelley and the radical English tradition. But it was black literature that began it for me."

His reading now ranges from Colin Channer's Jamaican novels - featuring "love, sex and a bit of philosophy with titles from reggae songs" - to George Lamming's essays, TS Eliot and Gerard Manley Hopkins, whose "strange diction really struck a nerve with me as soon as I heard it". But now, as from the beginning of his career, what motivates him to write is politics. "Writing was a political act and poetry was a cultural weapon - though my early writing was a load of rubbish really. I tended to use lots of 'thees' and 'thous', which is what I thought poetry needed." These early efforts soon progressed to unconscious imitations of Derek Walcott and then, more fruitfully, work influenced by Kamau Brathwaite.

"Brathwaite was so inspiring because he more or less subverted the whole canon of English poetry. There were elements of jazz, you could hear the drums, and the language of West Indian folk tales. This was about the Caribbean and the new world experience."

Johnson was aware that he was living through an exciting political period. "We thought we could change the world. There was the anti-colonial struggle in Africa. The civil rights movement had been followed by Black Power. There was the anti-Vietnam war movement." On a local level, being active in race and political issues in south London had its risks. His mother was concerned that he would come into conflict with the police. "Black people were being framed and brutalised, deported and imprisoned. People died in prisons. She felt as strongly as me about the racism we were facing, but she was more constrained in her response than us youngsters were."

Johnson was politically active while studying sociology at Goldsmiths, but by the early 70s, with the demise of the Black Panther movement, he felt there weren't any political organisations that he "could make a useful contribution to in terms of the revolutionary position I had envisaged. So I went through a sort of cultural nationalist phase. Part of that was an attraction to Rastafari, which was very alluring in terms of the subversion of the English language, the dissident philosophy, the anti-colonialism and the spirituality."

He tried to grow dreadlocks - "but I didn't have the right hair" - and began to work with a group of Rasta drummers with whom he found a distinctive poetic voice. "The music was a very important part of it. I remember loving this three-album set called Grounation by Count Ossie & the Mystic Revelation of Rastafari, which seemed to have everything. There was narration, drumming, chanting, jazz, poetry, oratory, history. It just freaked me out."

His involvement with Rastafarianism eventually foundered on the fact that, as an atheist, "I couldn't reconcile myself to the idea that Haile Selassie was God. And I didn't think the wholesale repatriation to Africa was either practicable or desirable as a political project." His politics progressed from Black Power to black working-class, and he joined Race Today. This collective published his early poems in its journal and then, in 1974, his first collection, Voices of the Living and the Dead. The following year, Bogle-L'Ouverture published Dread Beat an' Blood, although he says it was "a bit of an uphill struggle to persuade them. They thought it was too violent and people advising them said it wasn't good poetry. But in the end, they were persuaded and then things began to happen quite quickly. Dread Beat an' Blood was basically written for the stage, for voice and drums, so it was a natural step to record it as an album."

His work acquired increasing mainstream literary acclaim, but he didn't feel part of any tradition. "I really thought I was doing something new. It's not until later that you realise all trailblazers have trailblazers who preceded them. But there wasn't anyone else writing about the black experience in Britain in the kind of language I was using and from the aesthetic I was coming from. These were poems to read at rallies and demonstrations and cultural gatherings of a political nature. So when I was published by Penguin, it was a big thing." He is no longer on the Classics list - "when Milosz died, I became even more of an anomaly" - but is delighted to be reprinted on the mainstream Penguin poetry list. "I really don't want to be the only guy alive on a list full of dead people. I'm just middle-aged, you know. I've got plenty of time left and things to say."

He says his increasing focus on black working-class politics has allowed his work to speak to national and international audiences, including parts of Europe where there are very few black people. "It's not difficult to see parallels between the black working-class struggle going on in this country and things like Solidarity in Poland. Bob Marley wrote about Trenchtown, but people had no problem taking that to Birmingham or New York. I still begin with the particular, and hope to arrive at the universal."

Looking back over 30 years, he sees life for many black people as having been "one step forward, two step backwards. And sometimes the other way round." He points out that there are still too many deaths in police custody ("black and white"); that the recommendations of the Macpherson report - which charged the Met with institutional racism - are being whittled away; and that the old issue of stop and search is again on the political agenda. "And these things all still exercise me. Of course, it's great to be at the Barbican playing with wonderful musicians. I really enjoy performing to an audience who now bring their grown-up children to my shows. It's like life after death. But the thing I'll always be most proud of is when an old woman comes up to me in Brixton market and asks: 'Are you the poet?'"

Inspirations

The Bible
Derek Walcott
Kamau Brathwaite
Gerard Manley Hopkins
Count Ossie & the Mystic Revelation of Rastafari

· This article was amended on Tuesday March 11 2008. We misspelled the name of Kamau Brathwaite as Braithwaite in the above interview with his fellow poet Linton Kwesi Johnson. This has been corrected.