As recently as 1997, in her exhibition of The Quick and the Dead, Deanna Petherbridge, the professor of drawing at the Royal College of Art, explored for a London audience the relationship between artists and anatomy.

Four years later, the Arts Council followed with Spectacular Bodies. Both made the connection, particularly, with wax models of the human figure that were observations of skin, bone, organs, arteries and tendons in the most telling traditions of realism, informed by the ancestral aesthetics of art and craft. Both introduced us to the art of modelling in wax the three-dimensional complexities of the body, a by-product of sculpture in the service of medicine and surgery that flourished in the Age of Enlightenment and into the 19th century. That the best modellers were Italian (the best of their work still in Bologna and Florence) surprised no one acquainted with vermicelli and spaghetti.

The lofty intentions and achievements of these modellers were, alas, dreadfully debased as the 19th century wore on, and it is this decline into entertainment and amusement that the Wellcome Collection now explores. Only a handful of exhibits illustrate the dying continuity of their origin as art-into-science; a larger number are the worthy teaching aids made by Joseph Towne — a man with “a rigid regard for truth” rather than aesthetic appeal — for the benefit of medical students at King’s College (and still so); but most are the stuff of the circus side-show, appealing to the prurient curious to see the penis and vagina stricken by syphilis.

In this, the Wellcome does what only it can do without a blush. It is a scientific institution, not a gallery, and as with medicine itself, it has a duty to deal with the history of medicine. This waxwork business is part of that history, and if the current exhibition seems a thing of freaks, dwarfs, conjoined twins and the consequences of syphilis, so be it, for in these it embodies historic truths about our slippery and hypocritical attitudes to such misfortunes, pleading instruction on the one hand while enjoying smutty titillation on the other.

There are things of beauty in it — a life-size recumbent figure of a woman has its subtle moments in the contrast of flesh and linen, and an oddly pathetic note informs the face of a young man whose open skull illustrates hypotrophia, which I take to be enlargement of the brain (I wish that the labelling of this and other exhibits had been a trifle kinder to the medically ignorant), but, at the other extreme, it is the loin-clenching frisson of horror and disgust familiar in grand guignol that it induces.

Those who saw the Petherbridge and Arts Council exhibitions will recognise the virtue of the Wellcome’s completion of the tale they told, and in that sense this exhibition is important. On the other hand, it can be argued that this is an exhibition for the adolescent with a taste for the gruesome and macabre. Had I still godsons of that age, I’d take them to see the Rasputin-like peasant with a single Cyclops eye, the bearded lady, “the ravages inflicted on the unwary in the red-light district of Barcelona” and the “parade of Nature’s monstrous deformities” — and then widen their perceptions by whisking them off to look at real sculpture in the V&A.

I greatly enjoyed this exhibition and regret only that it is not twice the size.

Until 18 October. Information: 020 7611 2222, www.wellcomecollection.org. Open Tues-Sun 10am-6pm (Thurs until 10pm). Admission free.