She is the opera singer who shuns the limelight, hardly ever makes recordings and disdains PR with a wave of the hand. Her voice is unclassifiable, neither true soprano nor authentic mezzo, and her range of roles wildly contrasting. Yet somehow Anna Caterina Antonacci would be one of those artists who has both inspired a fake MySpace page (mostly affectionate, though it does mischievously describe the fortysomething singer as a “23-year-old swinger”) and has made no attempt to shut it down.

Perhaps that’s because in the increasingly promotion-heavy world of opera Antonacci really is that rare thing — a cult diva. “Cult?” she repeats, querulously, when I tentatively mention the word. “I never thought about it, but it’s great. I’m happy that I’m hard to get.”

It does feel a little bit as if I’m paying court when I arrive at Antonacci’s unshowy but chic apartment in Paris, where the lighting is subdued to the point of ceremonial gloom. That said, the singer herself greets me unceremoniously in her slippers, and her eight-year-old son is also at large. She might present a regal front, but that’s more a sign of a quietly private persona than any diva-like hauteur.

She is, however, uncompromising in her craft. When she arrives at the Wigmore Hall for two concerts with the English Concert (her first performances in the UK since her visceral and acclaimed Carmen at Covent Garden two years ago), it will be to repeat a rare concert feat: singing all the characters in Monteverdi’s dramatic cantata Il Combattimento di Tancredi e Clorinda. “It’s not so difficult,” she protests. “It’s not like singing Aida and Amneris in one night — but to me this piece has always looked like a monologue, a tale. It’s like in the Middle Ages when somebody arrived in the village and told the people some stories, like a show, or a newspaper.”

What audiences will hear at the Wigmore will actually be something of a slimmed-down version of Antonacci’s Combattimento, which last took place as part of a wildly popular staged show in Paris, itself forming the basis for her first (and so far only) studio album in 2006, Era la notte. “It was really a one-woman show,” she recalls. “A long tale about sorrow, a woman abandoned, and it ends with the love battle between Clorinda and Tancredi. It’s really something that comes from the deepest of me. ”

This is Antonacci’s sweet spot: the tale, the character, and she’s far more effusive on those challenges than the vagaries of the vocal art. “At first, the acting was always easier,” she confesses. “It was singing that’s always been difficult and risky. So for me the big question has always been: why didn’t I choose the actress way and leave the singing?” Pressing for an answer, I get a laugh and a shrug.

Comparisons with another intense Italian, the far more high-profile Cecilia Bartoli, are inevitable: in fact for a brief period in the 1990s the two were often considered rivals. “But Bartoli began as a recording singer,” Antonacci says. “She was 23 when she was chosen by Decca [her record label] and she had done nothing before that. But in the 1940s or 1950s you recorded to testify what you had done. Now, because they push you, it’s easier! It’s not your personal battle every day. Also, when you start with a name your fees are higher.”

The broadside isn’t so much aimed at Bartoli as indicative of what makes Antonacci’s legions of fans so devoted: how old-school she is, and how she chooses her own path. Growing up in Bologna, opera was her passion from childhood. But she began her career at 18 in the Bologna Opera chorus rather than music college, working her way through years of bit parts before any real success came her way.

There’s another contrast with the prodigious Bartoli, of course: the two are polar opposites when it comes to vocal style — which partly explains why Bartoli was snapped up by Decca at 23 and Antonacci had to wait until 2006 to get into the recording studio. Where Bartoli’s voice was (and remains) small-scale, focused and delicate; Antonacci’s is a wilder and, she admits, more unpredictable instrument. Early on she struggled with it. “I don’t think anybody thought I was a mezzo, but I didn’t have the technical means enough to be a soprano, so I had to arrange myself in the way I could.”

It was only in recent years that she says she has really hit her stride — thanks to her late singing teacher, Alain Billard. “He helped me to discover other roles, Gluck, for example, and Cherubini’s Medea, which before I could not even think about singing because of the range.”

The watershed performance, though, was as Berlioz’s deranged, prophetic priestess, Cassandre, in his five-act epic The Trojans, which cemented her reputation in Paris as the singer of choice for opera’s most conflicted heroines (it helps that this is another “in-betweeny” part, sung by both mezzos and sopranos). “That was the first, the biggest success, in Paris, but so unexpected.” Unexpected? “I don’t feel settled now. You have always to seduce the voice, to convince her to do what you want . . . and of course the careers don’t last so long. So when I’m asked for Carmen in 2012, I say, well, can a 50-year-old woman still sing Carmen?”

There’s talk of Antonacci returning to Covent Garden, again as Cassandre, but so far it’s just talk; a planned debut in New York is also off the cards after a small rumpus involving Angela Gheorghiu snaffling the part that Antonacci was originally promised.

In short, Antonacci is not looking much farther than she thinks that tricky mistress, her voice, will allow. Take her, then, exactly as you find her, even if she knows that “opera’s sphinx” isn’t exactly the monicker that’s going to propel her into the stratosphere. “I don’t know if that’s solvable,” she says, solemnly. “I have to accept that I’m something a little bit special, like Cassandre — a little bit strange, bizarre. So maybe I’m not one for the big, big public.” Never mind: it’s their loss.

— Anna Caterina Antonacci sings at the Wigmore Hall, W1 (020-7935 2141, www.wigmore-hall.org.uk), on Jan 26 and 29

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