Yaniv d'Or stands centre stage in a light suit, surrounded by his baroque ensemble, tapping a foot, virtually dancing to their introduction before breaking into song. He's a charismatic performer with a taut and energetic presence; and though he is a countertenor, he's an extremely unusual one, singing with full tone and natural, often unrestrained vibrato. With his enormous range of both pitch and colour, he sounds almost like an operatic tenor, but higher.

Unusually for a countertenor, too, he hails originally from Israel (though he is now a UK citizen). Much of the standard repertoire that countertenors sing is from the baroque era and often church-related; Jewish exponents are few and far between. "Every time I sing a Bach cantata, I wonder what my mum would say," d'Or admits wryly. "Or singing a Mass on a Sunday. She'd be shocked."

D'Or, 40, is coming to London's Wigmore Hall later this month to focus on early music of a very different kind. Entitled Latino-Ladino: Songs of Exile and Passion, it is a programme he has assembled through exploring his own heritage from the Sephardic diaspora.

The CD is a feast of fizzing rhythm, irresistible melody and dusky soulfulness, sourced from across the Mediterranean and as far afield as South America, and performed straight from the heart. "I call it 'folk baroque'," d'Or says. "Most of it dates from the same era as the baroque, but it was never written down. Instead it was passed aurally from generation to generation."

D'Or's ancestors were among the Jews who left Spain in 1492 at the time of the Spanish Inquisition. "They spread around Turkey, Italy, what was then Constantinople, and finally settled in Libya. My great-grandparents on my mother's side were from Benghazi and on my father's side from Tripoli. They emigrated to Israel when it was founded in 1948."

The songs of Latino-Ladino hold strong resonances for him. "My mother used to sing us this music when we were children. And when my father went to synagogue he would always sing in this high countertenor voice with all these microtones, and I was thinking, 'Wow, what's going on here?' When I was introduced to baroque studies, I realised that we are of Libyan descent, which is not far from Italy, so the theorbo and the oud are not that alien to each other. We like to do appoggiaturas in baroque singing and they have many similarities to the microtones that my mum used to whisper in my ear."

Born in Israel, he grew up in a traditional family with the practices of Judaism a vital presence; later he came to Britain to study and ended up staying. He currently divides his time between London and Tel Aviv, plus his international engagements. "Today I'm trying to build bridges with other people, beliefs and religions," he says, "but I still see and recognise all the beautiful parts of Judaism: the ability to love unconditionally, which I think is a very Jewish thing, and to give, always to be sharing. If you have a talent, just communicate it and make other people happy."

From the start, says d'Or, his parents ensured that their four children had music in their lives. "My father was a carpenter, earning next to nothing, and my mother was a housewife, but we all learned the piano since our very early days and we all sang," he says.

"My brother went into ethnic pop, and my sisters both played the piano and sang, but then decided there are too many musicians in this family."

D'Or stumbled across classical music by chance. "I was studying for an exam at school and I put the radio on to Voice of Music, the classical channel. They were playing some sort of madrigal, certainly polyphonic music. I remember, as a boy who wasn't at all exposed to classical music and liked Phantom of the Opera, being completely taken by it – as if I went 200 years backwards in time. The polyphonic singing made so much sense to me. And at that point I knew I was going to become a classical musician." He now presents his own programme on the same radio station.

Discovering his true voice, though, was more difficult. He started to sing as a boy soprano; his singing teacher detected when he was 16 that his natural ability was as countertenor, but not one like many others. Soon he had a fight on his hands.

"I was blamed for singing too naturally," he says. "For years I fought against conductors who told me I have too much vibrato. But I have a big voice. This is my voice, I can't flatten it! It won't sound like the typical, mellifluous counter-tenor. It can be rusty, high, squeaky or rounded, as necessary for the music. But just try persuading academies that this is the way to sing! I had so many fights with my teachers in London [at the Guildhall School of Music and Drama] and at the Jerusalem Academy. Still, a few people really believed in me."

In London, the pianist and vocal expert Graham Johnson was one of them. "He said to me: 'Look, you are wild. You have a wild voice. Don't let anyone castrate you! You just have to sing.' He gave me some Hugo Wolf songs to study, and some Alban Berg. I loved it - and I just sang.

"Today I'm so happy that the whole 'authentic' thing about singing with no vibrato has disappeared from the world," he adds. His next role, at the Opéra de Baugé festival in France, is the Emperor Nerone in Monteverdi's L'incoronazione di Poppea: an impassioned love story about a couple who will stop at nothing to be together. "I sing it like there is no tomorrow," d'Or says. "I scream, if needed! And that's OK." Further roles coming up include Oberon in Benjamin Britten's A Midsummer Night's Dream, Handel's Giulio Cesare and a CD of 19th- and 20th-century Lieder by Schumann, Duparc, Debussy and others.

It was after performing in Josef Bardanashvili's opera Journey to the End of the Millennium, in Tel Aviv in 2005, that d'Or felt inspired to begin exploring his own heritage in more depth. In 2008 he assembled a new international group, the Ensemble NAYA; several years later they recorded a debut CD, Liquefacta Est, involving sacred and secular Jewish texts and instruments from east and west. It was chosen by Gramophone magazine as one of its Top Ten discs of the year.

To create Latino-Ladino, he says, he began by working with Amit Tiefenbrunn, music director of the baroque ensemble Barrocade. "We met for a year to do jam sessions with these traditional Ladino songs, at first just with guitar, viola da gamba and voice. We realised we are doing very instinctive things: we knew when it felt right and when it didn't."

Not all the music in the project originates in the baroque: a couple of numbers are familiar as Spanish classical guitar pieces, and one extraordinarily beautiful song is a composition by d'Or himself. "I was in Israel on "black Friday" during the Gaza war two years ago," he explains. "I felt so lost. I felt I can't take it, so much death around me. My eye caught this beautiful text, 'The Loneliness of the Night', which says 'My soul is empty and all I want is to disappear and die'. That's what I tried to reflect by the piano at 3am. I set it in a baroque style, almost a minuet - as if constantly dancing with death. That's how it felt."

Eventually he approached Manuel Mohino, producer for the conductor, viol player and baroque authority Jordi Savall, to see if he would work with them. "He invited us to record in Belgium, and everything came together. We all felt satisfied that we had achieved our goal."

D'Or's larger goal, though, is about bringing people together through music, reaching beyond ethnic, religious and cultural differences to find shared roots and the same emotional heart.

"I cannot say things as politicians do," he declares. "But I can sing them. I can communicate them from the heart in the line of melody, and I see the reactions when we perform. In Croatia a few years ago we performed Liquefacta est and a Bosnian lady about 95 years old came backstage after the concert, completely tearful. She said: 'I'm not Jewish, but I know this music: my mother used to sing it to me…' And I realised that this music travelled, crossing boundaries between religions, countries, continents.

"It's my way to communicate with people," he declares. "I don't care about their sexuality, their religion, their ethnicity. We are all human, we all have the same feelings. It's liberating to feel that way. I see a wave of nationalism washing so much of the world, and I feel so lost - because instead of bringing people together, everyone grew apart and created fear. I'm hoping that music can overcome it. I'm a citizen of the world, singing for people, not for borders. It's all about the music: just close your eyes and let your soul fly!"

Yaniv d'Or launches Latino-Ladino at the Wigmore Hall on 26 June. The CD is released the same day.