John Stezaker, Whitechapel Art Gallery, London

Take some old film portraits, cut, and paste together. Hey presto, you've got a cute Hollywood in-joke – and one of the saddest and cleverest shows in town

And so, for no very good reason, to Meret Oppenheim's fur-covered teacup, Object.

How does it work? In the functional sense, presumably it doesn't. Oppenheim has taken two markedly proper commodities – teacups and fur – and run them together to make a third, improper one: the phrase "drinking from the furry cup" might have been coined for Object. Like all surrealist artworks, the power of this one lies in its coincidence of inappropriate things, and that in turn relies on time. See a Chinese gazelle's hide and then, a moment later, a teacup and you will not turn a hair. But see a gazelle-hide teacup – a gazellehideteacup – and you might find yourself retching.

John Stezaker makes collages out of found images, mostly old film stills and studio publicity shots, sometimes with the addition of vintage postcards. Like Oppenheim's teacup, his work depends on coincidence and its Freudian friend, accident. As with Oppenheim, too, you might reach for the word "Surrealist" to describe Stezaker and his art, although Object was made in 1936 and the earliest work in Stezaker's one-man show at the Whitechapel dates from 1976, long after Surrealism's heyday. There is probably an -ism to describe what he does: neo-Surrealism, perhaps, or post-neo-Surrealism. As Molesworth might say, I neither kno nor care. There are other, more important words to apply to Stezaker's work, among them "elegant", "cunning" and "uproarious".

Take this one, from a series called Marriage (Film Portrait Collage) and made in 2006. Stezaker has taken two black-and-white studio photographs from the 1950s, one of a man, one a woman, cut them diagonally down the middle of their subjects' faces and stuck them back together. Simples! Well, yes and no. In terms of cutting – a big part of the collagist's work – Stezaker is oriental in his simplicity. There is the single slice, made, at a guess, with a craft knife, the collaging of two parts only. Where the work comes in is in the looking: in Stezaker finding the images and somehow keeping them all in his head, remembering how big they are and how saturated, what angle they were taken at, how they will slot in technically. And that is before the whole question of what will emerge, in emotional terms, from putting them together, how appropriately inappropriate they will turn out to be.

In the case of this particular Marriage, what hits you is its worrying beauty. The man and the woman are individually lovely, but the troubling thing is that their beauty is the same. Seen as one, she is revealed as strong and handsome, he as lush-lipped and feminine. This is less a marriage than a genetic splicing, a teacup of fur. Beyond that again is a story, unspoken but none the less told, to do with inconstancy, the tendency of all things to slide.

One suite of Stezaker's collages is called Betrayal, apparently based on a complaint common among male-to-female transsexuals that their hands give them away. The images in this suite are accordingly full of hands. But Betrayal would make a good working title for all of Stezaker's collages, their juxtapositions betraying all kinds of unsaid things.

What really brings you up short is the ease with which Stezaker seems to do what he does. My wordy paragraph above described one slice of his Stanley knife. That, though, is positively baroque compared with his pasting of postcards to publicity stills.

Here is one called Pair IV (2007), in which Stezaker has stuck a postcard of the Aar Gorge over the shot of a pair of suavely dressed movie stars, presumably gazing into each other's eyes. The gorge's two cliff-faces become the faces of the actors with such ridiculous accuracy that, as often with Stezaker's work, you find yourself guffawing out loud. It is like the unpicking of a metaphor of love, some cheesy, Hollywood line to do with elemental forces and the earth moving, chasms being bridged. You can almost hear the violins.

But there's something there as well as humour, as well as Stezaker's uncanny eye for visual coincidence. The oddest thing about Pair IV is that you feel it is strangely revealing of something, although it is impossible to say quite what. And so with Love X, in which a pretty starlet's face has had another slice of itself inserted across the eyes, so that each pupil is a pupil-and-a-half. It looks like she is batting her eyelids, or maybe as though the film has jumped on the projector. It's funny but also sad, heartfelt but very, very clever. Do see this show.

Next Week:

Charles Darwent roams the subconscious with Susan Hiller at Tate Britain

Art Choice

The son steps out from his father's shadow in Lucien Pissarro in England, at the Ashmolean Museum, Oxford (to 13 Mar, above), which shows the illustrated books the artist printed with his wife. Hilary Lloyd's video art looks close-up at the everyday, prompting reflection on the technology of video at London's Raven Row gallery (to 6 Feb).