We catch Gilles Peterson's latest signing (and Cuba's finest new musical export), Daymé Arocena, in action, and speak to her about how she's rewriting the script of classical Cuban jazz.

"I once dated this guy who said I was 'dramatic', but my only drama is in my music," declared Daymé Arocena half way through her set at Saint Pancras Old Church earlier this year.

A sense of the theatrical was evident from the get go. Her band (bassist Neil Charles, producer Simbad, percussionist Oli Savill and the ferocious pianist Robert Mitchell) settled into the instrumentals of the opening number Nuerva Era, and we heard her before we saw her - a sweeping clarion call of a voice offering devotions to her orishas Ochun and Yemaya. It was magical to witness this woman, dressed from head to toe in white, cry out in worship to ancient African deities in a church building, where free mojitos on offer on the front door. But being Cuban, the syncretism of the moment probably didn't faze her.

Mounting into a crescendo, her voice - as it would do several times during the course of the night - strayed into improvisation that was as beautiful as it was bizarre - this time treating us to dolphin-like screeches. There were moments when she let her rich voice carry, her mouth left hanging open as the notes echoed around inside it, and around the church hall too. All of this swirling momentum culminated in a playful, "good evening" - a telling smile spreading across her face with the knowledge that she had her audience exactly where she wanted us.

Simply put, Arocena is a majestic performer, and all the more so the impressive because she is only 22. Addressing her attentive congregation, she declared her joy at being able to share her music as a "young, black... and international performer." Her rendition of 'Madres' was particularly spectacular, her conductor routes apparent as she led the band, setting the pace with wicker shakers, cow bells and that powerhouse voice.

Signed to Gilles Peterson's Brownswood label, she trained as a choir conductor for a decade, from the age of 10. "Cubans study music - classical music - from a young age", she observed when we caught up with her after the show. "I studied a lot of Bach and Beethoven, and still compose a lot of classical music for choirs and cello quartets, but I really wanted to be a singer. People would say to me 'Why do you want to be a popular musician? You can get that kind of stuff in the streets!'".

There are echoes of the so-called stuff of the streets - rumba, hip-hop and popular music in her sound. It's a testament to her maverick spirit that she hasn't let such attitudes prevent her from crafting the kind of music she wants, irrespective of these cultural, and to be frank, arbitrary, borders.

Her openness is evident on the track 'Nino', which began with a beat box, before collapsing into a gentle clockwork lullaby dedicated to her younger brother, sliding across the scale to more a hip-hop tinged, Flying Lotus-style incarnation of jazz. "I try to take influence from everything," she says when asked about her inspiration, "I won't say that I don't like hip-hop, so I won't listen to it. It's important to always listen, so I'll study hip-hop. Maybe they are talking bullshit, but if they can get the attention of a lot of people, then they have something - so I'll listen and learn and use it in my music."

'Sin Emprezar' is the "saddest song" she'd ever written, a brooding neo-soul track carrying flavours of Sade. Her improvising saw her voice take gymnastic leaps across deep baritone notes, animated ad libs that ended with vocal guitar 'wah-wahs' that Prince would be proud of.

There's a real playfulness in her songwriting - numbers filled with innuendos and the ability to craft narratives around unlikely sources of inspiration, bringing to mind old lackadaisical ditties from the likes of Louis Armstrong. She even laughs along to her own anecdotes like Ole Satchmo too. Dust was a case in point, a track about grinning and baring through the aggravated asthma she endured whilst staying at the dirty, dusty home of a friend "I couldn't tell them!" she divulged through her wicked, raucous laugh.

Her newest single, the soulful 'Don't Unplug My Body' saw her leading the audience in a spontaneous a cappella, before a spectacular encore with El Ruso. The church bells joined Arocena with her cow bell as she cascaded down the aisle, her white skirts flowing about her as her voice stormed through the building one last time, ringing out in Yoruba, Spanish and English.

"Cuba is a muuusiccal country," she explained, half singing, "it's like the middle of the world. Hundreds of years ago, boats would come from different countries and would stop in Cuba for rest - and [new groups] would leave something behind, so even though we are two small islands, you can get all kinds of music.. .someone once said that Cuba is like soup. Our music is influenced by everything and it's the most beautiful thing we have. We are so mixed - you can see a beautiful Chinese man and he is Cuban; or see a beautiful white man with blue eyes, and he is Cuban too."

It's a slightly romantic version of Cuba's history. There's no doubting the nation's diversity, but some those boats would have been carrying slaves who brought with them the faith that Arocena herself is devoted to, and the rhythms and chants that feature so heavily in her music. There's a strange sense of doublethink and cultural amnesia that allows African rhythms to have infiltrated so much of Cuban music, and yet still be frowned upon by those who see European music as superior, in keeping with residual racist attitudes. Even the Cuban revolution to an extent, with all its anti-racist rhetoric, inadvertently put Afro-Cuban music in a disadvantageous position by shutting down music ventures in the '60s and forcing many musicians to seek work in exile.

All of this contributes to heightening Arocena's importance as a contemporary Cuban artist - especially when considering that earlier this year, Cuba's musical giants, The Buena Vista Social Club, bid the world farewell (again) on their curtain call tour. Her pride as a black artist (as she remarked during the show), the visibility of her faith, and her ability to bridge the gap across genres serve defiantly as poetic justice in the face of Cuban history, as she fills these niggling voids with her talent.

"My music is a little classical, and jazz is the right bridge between classical and popular music," she reflects, "I think we should try to understand music as music, just to get better."

Watching Daymé Arocena and her band - you felt hopeful that you were witnessing the birth or growth of something electric - a new generation of Cuban artistry strong enough to bridge latent cultural divides in Cuba, and resonate with worldwide audiences.

Self-possessed, and all your diaspora jazz dreams come true, her musical drama is just getting started.

Daymé Arocena's new album, Nueva Era, is out now on Brownswood Recordings.