Shell-shocked by a bombing raid in 1944 Hanover, a German woman apparently conceived, or cloned, a child entirely by herself.

When such a process occurs, rarely, in insects and flowers it is known as parthenogenesis — literally “virgin birth”.

The story may not, of course, be true. But in the world of opera the facts never spoil a good myth, and this latter-day “immaculate conception” clearly has mythic potential. Not just in its echo of that other Virgin Birth, but because it seemingly happened in a Germany where scientists were already tampering with genetics.

You can see why James MacMillan, the most overtly Christian of modern-day British composers, would be attracted to the story.

And for the one-act opera he wrote in 2000 (after discussions with the Archbishop of Canterbury) his librettist, Michael Symmons Roberts, supplied a text rich in biblical Annunciation references. Indeed, the whole piece is a dialogue between the woman and a “fallen angel” — called not Gabriel, but Bruno.

Bruno seems at first to harbour sexual designs on her, but then brusquely declares that she will give birth to a daughter who will have no father.

It’s that daughter who, on her deathbed, acts as an ironic narrator (Charlotte Roach, gamely attached to life-support tubes) — mulling bitterly over her weird life as her mother’s doppelgänger.

Clearly there’s a strong “don’t play God with genetics” message lurking here, and that’s reflected in MacMillan’s music.

The desultory electronic plinky-plonk we hear before the curtain goes up is apparently based on the letter sequence of the human chromosome. It’s been unravelled by science but (MacMillan seems to ask) to what soulless purpose?

But most of MacMillan’s score, which is superbly played by the Britten Sinfonia under the composer’s direction, is much more jolting, visceral and jittery: harsh, quickfire bursts of instrumental dissonance, or sweet, smeary consonances that are, if anything, even more disconcerting.

On top of that the two singers (Amy Freston and Stephan Loges, both admirably intense) are given histrionic melismas — richly expressive, except that they often obscure the very words they are meant to illustrate.

Happily, Katie Mitchell’s staging — the opera’s first — resists the temptation to pile more symbolism on to a piece that already totters under elliptic nuances. Instead she plays the work, in Vicki Mortimer’s ingenious dual-era set, as a kind of theological film noir — Raymond Chandler meets Dan Brown — with spookily blowing curtains, flickering lamps and frenetic bursts of activity.

Bewitched, bothered or bewildered, you’re in and out in 50 minutes.

Box office: 020-7304 4000, to June 18

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