Walking on Hampstead Heath the December before Covid, I got caught up in a festive party of bichon frises dressed, like their owners, in Christmas jumpers. It seemed bizarre at the time but wouldn’t surprise me now. During lockdown the local dog population exploded and the smaller breeds now wear jumpers all winter.

There are no dogs in jumpers in the Wallace Collection’s new show – though, given the level of anthropomorphism, there might as well be. The ‘Allegorical Dog’ section, devoted to Edwin Landseer, includes ‘Trial by Jury’ (c.1840) with a poodle sitting as judge, and a canine interpretation of the parable of Dives and Lazarus featuring a well-fed St Bernard guarding a bone from a hungry terrier (see below). ‘None but Landseer can thus render the human in the canine expression,’ enthused the Times when this painting, ‘Doubtful Crumbs (1859), was shown at the Royal Academy. As a comment on inequality it now seems in doubtful taste – if not as tasteless as Landseer’s ‘Uncle Tom’ (1857), a canine condemnation of slavery with Harriet Beecher Stowe’s hero played by a chained black pug.

A surfeit of Landseers may not be as fatal as a surfeit of lampreys, but it can’t be good for one’s mental health. It’s probably no coincidence that cat-fanatic Louis Wain and Landseer both went mad: anthropomorphism messes with your mind. Thirteen Landseers in a show of 59 works felt like an overdose, though Queen Victoria couldn’t get enough of them. After the Duchess of Kent commissioned him to immortalise her daughter’s King Charles spaniel Dash in 1836, a dozen royal pet portrait commissions followed.

All the works in this show are from British collections, so there are no Jean-Baptiste Oudry portraits of Louis XV’s favourite hounds. There are some fine George Stubbs portraits of aristocratic working dogs, but the only French painting is by Jean-Jacques Bachelier – portraitist by appointment to Madame de Pompadour’s pooches – of a toy Havanese with its topknot tied in a pink ribbon begging in front of a velvet-upholstered niche à chien.

It was royal women who started the fashion for low-slung dogs. Victoria, under instruction from Landseer, produced a sprightly watercolour of her dachshunds Waldina and Waldmann that bears comparison with Hockney’s portraits of his beloved Stanley and Boodgie. (Our own late Queen’s penchant for short-legged breeds is remembered in a room off the shop hung with photos of royal corgis.) The fashion for Pekineses started after Victoria was presented with one called Looty, looted from the Summer Palace in Beijing in 1860. A later arrival, Ah Cum, smuggled out of China in a crate, was stuffed and donated to the Natural History Museum. He is upstaged in the exhibition by Minnie the Lulu terrier, preserved by her bereaved owner like a sainted relic in an inlaid cabinet full of artificial flowers.

Taxidermy was one way the Victorians memorialised their dogs; another was brooches set with miniature portraits, sometimes containing a lock of the deceased’s fur. But the most touching memorial here is a modern one: Lucian Freud’s painting of his whippet Pluto’s grave, covered in autumn leaves (2003), hangs beside a portrait of its occupant as a puppy (1988). Leonardo’s studies of a dog’s paw in the exhibition were, one suspects, drawn from a dead model but for scientific rather than sentimental reasons.

There are too many ladies in this show, and not enough tramps. Only Lord Byron’s dog Lyon, depicted by Clifton Tomson with bristling fur and lowered head (1808), looks remotely dangerous; Byron joked that the wolfhound ‘doted on me at ten years old, and very nearly ate me at twenty’. The mongrel lying contentedly on a ledge in an anonymous Spanish 17th-century painting is said to be a street dog but looks far too glossy-coated and relaxed for that. My guess is that his artist master, bored with still life, cleared the ledge of his usual crocks to pose his dog on it.

Artists’ dogs, unsurprisingly, get the best portraits – Gainsborough’s ‘Tristram and Fox’ (c.1775-85) win the rosettes in this dog show. As alter egos of their master and mistress, their portrait hung over the family mantelpiece: whenever Gainsborough was in the marital doghouse he would send a grovelling letter in Fox’s name addressed to Mrs G’s spaniel Tristram and have it delivered by Fox.

It’s a funny feeling finding yourself in a gallery lined with dog portraits, like attending a canine Saturnalia where the dogs are the masters. Appropriately, the stars of this show are Roman. Forget Landseer: the first- century marble sculpture of a greyhound bitch resting a tender paw on her mate’s shoulder while affectionately nibbling his ear is the most human image in the exhibition. So why is it normally hidden in the stores of the British Museum? Inspection of the dog’s undercarriage perhaps reveals the answer. Dogs will be dogs.