Ordered to sing for the Princess of Wales, Velluti replied haughtily: “My throat deserves a queen”. Implored by impresarios across Europe to perform in their theatres, Marchesi would comply only if he was guaranteed an entrance on horseback to a trumpet fanfare, sporting a helmet with plumes at least a yard high. And when Farinelli produced one of his most sustained streams of beautiful sound on the London stage, a besotted female fan was apparently moved to cry: “One god, one Farinelli!”

These fêted icons were the great castrati, and the new exhibition at the Handel House devoted to them, Handel and the Castrati, begins in grisly style. The first thing encoutered by visitors to the Brook Street museum in London are a pair of rusty castratori, the ghastly implements used on thousands of boys in 17th and 18th century Italy. “Like a pair of superannuated secateurs,” remarks the exhibition’s curator, Nicholas Clapton, a phrase guaranteed to chill any man’s blood no matter how breezily Clapton delivers it.

How could such horror lead to such beauty? When it comes to the castrati, the closer you get to the enigma, the more enigmas you seem to discover. A baffled 18th-century visitor to Italy, Charles Burney, reported: “I enquired throughout Italy at what place boys were chiefly qualified for singing by castration. I was told at Milan that it was at Venice; at Venice that it was at Bologna; but at Bologna the fact was denied, and I was referred to Florence; from Florence to Rome, and from Rome I was sent to Naples. All the Italians are so much ashamed of it that in every province they transfer it to some other.”

Church law forbade mutilation; shame drove the Italians to cover up a practice in which only they took part. But nothing could prevent the irrepressible rise of the castrato. Offered the chance to see their sons “transformed” into richly rewarded singers, many impoverished Italian families struck deals with local talent scouts and did their best to cash in on the future profits that their mutilated sons might be able to make. Not that many did — only 1 per cent, estimates Clapton, ever joined the premier league of a Farinelli or Marchesi — but the tantalising possibility was always there.

Driving the industry were two crucial developments. The popes had banned women from the stage and from their choirs, ensuring a constant demand for male sopranos and altos. Secondly came the development of the baroque opera seria. “People were experimenting with new forms of vocal music,” says Clapton. “It was a lucky accident of history that these voices which were capable of an extraordinary amount of expression came along just when a new form of theatrical presentation arrived.”

It’s certainly appropriate that the Handel House is playing host to one of the first exhibitions devoted to these artists. Handel’s operas and oratarios contained what was arguably the finest music ever written for the castrato, as well as some of the most challenging, and the exhibition focuses on the men who thrilled London with the maestro’s music.

Gaetano Guadagni, for whom Handel was moved to rewrite the Messiah, stares out from a lavish portrait, his eternally boyish features startlingly clear — as well as the strangely-lengthened torso that was typical of a castrato. “Their bone joints didn’t harden,” explains Clapton, “so their ribs kept on growing and the lungs expanded to fit.” It’s another ghoulish explanation for a breathtakingly beautiful effect: the castrato’s astonishing breath control and vocal fluidity. Handel turned his arias into show-stopping feats of vocal endurance and near-hysterical intensity.

The unspoken question behind the castrato’s sensuous trill was whether he could play the seducer off-stage as well as on. Caffarelli, the first to sing Handel’s Xerxes, certainly seems to have managed it. Caught in flagrante by his mistress’s husband, he fled to her back garden for the night, bringing on a bad case of rheumatism.

It wasn’t just the cuckolded husbands who resented the castrati. A magnificent engraving displayed in the exhibition presents a monstrous caricature of the two great rivals of the early 18th century: Senesino and Farinelli. With their tiny heads and absurdly over-extended bodies, they both tower over the petite soprano. And the satirists were not alone in their ridicule. Where the Italians called the castrato “virtuoso” or “primo uomo” [first man] the sceptical French were more likely to label them eunuchs or cripples.

When Niccolini left London, one anonymous English commentator wrote: “May Great Britain no longer be corrupted by frivolous trilling. May your eunuch’s voice ring out there in that country where lust and dissolute behaviour prevail.” Loathed and lusted after in equal measure, the quintessentially exotic castrato inspired reactions as ambiguous as the nature of his craft.

By the time of France’s invasion of Italy the conservatoires that had pumped out castrati were in decline. A new sound was in the ascendant: the tenor. “Like the castrati in 1600, it was irresistibly virile — and new,” Clapton says.

The practice didn’t quite die out, but the last castrati were shadows of their former selves, more likely to be pitied than idolised. What remains are the accounts of an unearthly skill that cannot be replicated — and a rusty pair of secateurs.

Handel and the Castrati opens today at the Handel House, W1 (020-7495 1685)