David Shrigley's exhibition at Hayward Gallery, London. Photograph: Linda Nylind for the Guardian  A man is asleep. His little hands grasp at the blanket as he utters all those little noises and mumblings that make the human animal so endearing, so deeply annoying. Dreams and emotions cross his face, drawn there, then erased. This is not Warhol's famous movie Sleep, but a looped animation by David Shrigley with the same title. The drawing has great economy, a cack-handed eloquence. I wait for the man to wake or die or scream, or for the blanket to betray some involuntary erotic protrusion. It doesn't.  Shrigley's art now fills the top floor of the Hayward Gallery in London for his new show, Brain Activity, which opens tomorrow. Drawings, sculptures, animations and photographs – I go from room to room constantly seeking out the next excruciating gag. But does his art last? Is it funny the second time round, beyond the spark and the laugh?  I own a Shrigley and I look at it several times a day. I keep it with me always – and often flash it at people. It's a tattoo. The artist drew it on my body at the Frieze Art Fair a couple of years ago, and I had it made permanent. "Writing," it says, in Shrigley's wonky script. It's written on the body, on the stomach, to be precise. If ever I'm lost in a daydream, I give it a glance to remind myself what I am supposed to be doing at my desk. Writing.  There's more to Shrigley than his knowing nods to high art, although his 194cm-tall bronze finger looks a bit like a late Giacometti or Brancusi's Bird in Space (well, it's tall, thin and made of bronze, at any rate). And there's a drawn outline of a curly stemmed pipe with the inscription This Is Nothing; Magritte's famous pipe, on the other hand, was annotated with the words This Is Not a Pipe. A song on the 7in vinyl disc that comes with Shrigley's excellent exhibition catalogue has a man yelling: "Get out of my house." It bears more than a passing resemblance to Bruce Nauman's sound piece Get Out of My Mind, Get Out of This Room. The Nauman, you might argue, isn't as danceable. One can go on and on with the art references, from Munch to Martin Creed.  Shrigley's bleak, black humour and sophisticated grimness make you wonder about the mind that made this work – crazy guy, crazy art, you think. But Shrigley in person is mild, polite, ostensibly English, though he has worked in Glasgow since studying there two decades ago. Yet much of what he does gives the impression of having been produced by a madman sequestered away in a locked ward, sending out messages under the door.  What this exhibition misses out on – unlike Shrigley's books of drawings and photographs – is the relentlessness of his art. He produces thousands and thousands of drawings, most of which fail his scrupulous quality checks. What counts for quality in his work is actually the appalling, the abysmal, the painfully dire. When he starts making highly crafted objects, I like his work somewhat less. The giant ceramic cup and saucer, filled with gallons of fresh tea each day, feels laboured to me. The stuffed ostrich with no head? No. The fishing waders filled with expanded polyurethane foam – standing up on their own, drooling solidified goo, and called (inexplicably) Cheers – work rather better, but don't ask me how.  Little stick people screwing on a real car bonnet? No. And rearing up behind this is a giant and very characterful wall drawing of a man, the body parts all inappropriately labelled; meanwhile, the pink thing I spy through a small hole drilled in the gallery wall is fun, whatever it is. I shan't spoil it for you.  Shrigley's work is very wrong and very bad in all sorts of ways. It is also ubiquitous and compelling. There are lots of artists who, furrowing their brows and trying to convince us of their seriousness, aren't half as profound or compelling (I can provide a list, on receipt of a postal order). His work is a kind of corrective, a dissection of the human condition. He would have had Beckett in tears; and that Austrian master of miserabilism, the writer Thomas Bernhard, might even have cracked a smile.  It doesn't much matter if Shrigley is or isn't a Big Heavyweight Artist. He's brilliant anyway. I keep thinking he could have made a less polite exhibition. I wanted more stuff and less art, something that would delay me longer. But his work isn't really lip-pursing or ruminative. We look, we wince or laugh, and we move on – in life as well as in art.
David Shrigley's new show is appalling, abysmal and painfully dire. But Adrian Searle likes his work so much he got it tattooed on his belly