“Since I was 19 I’ve been living in England and thinking I’d go home, but there was a point, around six years go, when I realised I’m here now: I’m black British.” So says Roger Robinson, who this week won the TS Eliot prize for A Portable Paradise, a poetry collection born of this realisation.

Furious laments for the victims of Grenfell Tower are followed by a crisp snapshot of idealistic young Jamaicans disembarking from the Empire Windrush in 1948, and a didactic sequence about the legacy of slavery today. A moody evocation of riot brewing on the south London streets sits alongside a love song to the National Health Service, which saved the life of his own prematurely born son.

It was the arrival of this baby – “just the 1kg of him / all big head, bulging eyes and blue veins” – that prompted both his acceptance that he was here to stay, and his investigation of the possibility that paradise might be portable. “I thought I’d look at the utopian idea of paradise, which is so important in this country, and then it began to mean a lot of different things – hope for my son, and the paradise that was denied to the people of Grenfell who had come looking to build theirs here and died because they weren’t in a position to do so,” he says.

A musician and cultural activist as well as a poet, Robinson is no stranger to public interventions. In 2018, he launched a Twitter appeal for 100 poems protesting about the mistreatment of the Windrush generation. He also recorded an eight-minute music track for BBC Radio 3, Survivor (For the Grenfell Survivors). “I’ve lived in tower blocks so I know what it’s like to live there and the community who do,” he says. “They’re not all immigrants and not all poor, but they’re all trying to build a better life and get out of there. It wasn’t that I was poor, I just didn’t have lots of housing opportunities. So when Grenfell happened I felt it viscerally.”

Robinson’s own relationship with England doesn’t follow an obvious narrative. Now 52, he was born to Trinidadian parents in the east London borough of Hackney “due to the system of opportunistic parents who always had a plan for you to go to university here”, he chuckles. When he was three years old, they returned to Trinidad, where his father became a PR executive for an oil company – “one of the first black men to rise that high” – and his mother worked as a nurse. His father encouraged him with comic book versions of the classics, while his mother is “an incredible storyteller. To a certain extent my poetry came out of her storytelling at the dinner table.”

He went to one of Trinidad’s top schools, where expectations were high and his teachers included the playwright and later government minister Ralph Maraj. “It’s impossible to make a living as an artist in Trinidad because it’s so small, so a lot of the teachers were artists who had returned from studying abroad.” At 19 he returned to the UK, initially to live with his grandmother in Ilford, Essex. “Now that was a real culture shock. I couldn’t feel at home there.” He soon found that Brixton was more congenial, forming a bond with the south London district that remains strong, even since he has forsaken its tower blocks for a three-bedroom house in Northampton, where he lives with his wife and their six-year-old son.

“Beware these hot nights in Brixton,” opens one observational poem, which is charged with the threat of urban unrest. “Ashes to Fire” was partly inspired by a night in 2011 when Robinson was dropped off in Brixton on his way home from a gig just as the London riots were starting. In a collection notable for its tonal and generic variety, this poem stands at one extreme – a thrumming reminder that he started out as a dub poet, and that dub “is the poetry of working-class suffering and protest”. He has also released five albums, and is the lead vocalist for his band, King Midas Sound, for which – surprisingly, given his rich bass speaking voice – he often sings in a high tenor that spills into falsetto.

He began to make his name on the London poetry scene in the 1990s, eking out a living by doing workshops in London schools. “It was a time when many schools were thinking about role modelling,” he says. “I was trying to convince kids – mostly young black boys who were not doing well at school – that poetry could touch their lives and reading could be useful to them.” He looks momentarily bashful behind his grizzled beard then adds, “I dress relatively decently now but I used to be a bit more urban swaggering.”

His belief in mentoring was rooted in his own experience. “I have had many mentors and one of them was [Booker prize-winner and poet] Bernardine Evaristo , who said: ‘You’ve got talent but you need to hone your craft.’” By his mid 20s he knew that he wanted to be an artist, and that if he was going to succeed he would have to live frugally. “My mentors taught me that if you control your economics you can control your output.”

I was told if you get less than 36 rejections don’t say it’s not working. On about my 37th attempt I got published

Evaristo was working for the writers’ support agency Spread the Word and, crucially, offered him the chance to attend free workshops, which he snapped up. During one, he met the poet Kwame Dawes, who urged him to broaden his reading. “He introduced me to Chinese and Russian and European poets. At the time I was only reading what I liked. They weren’t all black poets – I was into Seamus Heaney – but I was reading for culture; he made me read for craft, and think about why things worked.”

Dawes also told him: “‘If you get less than 36 rejections don’t come to me and say it’s not working.’ On about my 37th attempt I got published.” His first two pamphlets, Suitcase (2004) and Suckle (2009), were put out by another of his mentors, Nii Ayikwei Parkes. Portable Paradise is his fourth collection and, he says, “it began to shape itself in a way that was beyond my authorial control”, coming together so quickly that he was adding and removing poems until the day it went to press. (Even some of the poems in the ebook version didn’t make the printed book.)

Beneath the idea of paradise lies the concept of prayer, whether this involves the refusal of an Afghan immigrant to accept the substitute of therapy – “If it is Allah’s will, who is he to unload his burden on someone else?”– or Robinson’s own fervent prayers for his newborn son to be spared. The collection’s two dominant impulses, observation and entreaty, come together in fortuitous ways, and never more so than in the name of the nurse who cradled his son in neonatal intensive care, which becomes the title of the most overtly moving poem, “Grace”. Was she really called that? Yes, yes, he insists. He occasionally spots her driving around, though he has heard she has recently retired.

Which brings us to the question of his own faith. “I am Christian. I say prayers, but I don’t get to church much,” he says. Faith, for Robinson, is tied up with an idea of community and service. “So many people came up to me after the [TS Eliot prize] readings and said: ‘My child was premature, you expressed exactly what I felt.’ I want these poems to be useful and to help people to practise empathy.” Demonstrating how a prayer might work to achieve this, he quickly improvises one that could also be a standalone poem: “If you want people to understand the power of prayer in a time of trauma, let this book spread.”

• A Portable Paradise is published by Peepal Tree (£9.99). To order a copy go to guardianbookshop.com. Free UK p&p on all online orders over £15.