Charles Avery, Parasol Unit, London

It is easy to forget how important story-telling used to be in painting, how often its subject-matter used to consist of endless variants upon well-told tales from classical mythology, scenes from the Bible, the haughty and cocksure nature of kingliness (and queenliness), or just the lovely serendipity of everyday life.

Then came abstraction, which tried to deal a hammer blow to storytelling. For a while abstraction almost succeeded in convincing us that paintings should primarily deal with such rigorously arid matters as the physicality of paint and the act of painting. But only for a while because, well, nosey-parkerish human beings were finally wielding the brush.

In recent years, story-telling has made a big comeback in, for example, the drawings of Paul Noble. And now we see that another British artist, Charles Avery, has been up to something similar. Avery has been working on his story-in-pictures and objects and words, collectively entitled The Islanders, for four years. It isn't finished – it may never be finished – but what we see at Parasol Unit is a kind of pulling together of many of the constituent parts of it – drawings, paintings, objects, maps, creatures, together with dozens of others bits and pieces. The project reminds you of Gulliver, and how he chanced upon marvellous things when sailing out to sea.

Avery arrives, quite by chance, at an island that he believes to be uninhabited. It's not. Fascinated by how it differs from the world he has always known, he begins to draw and to describe those differences. Like any plundering anthropologist-cum-archaeologist, he brings stuff back from this magic place to show us how the world he has chanced upon differs from our own. Of course, like Swift, what Avery is really doing is using his "discoveries" as an opportunity to satirise our own world. So the success of the project hinges on two elements – the descriptive wall texts, which explain the nature of the world he has discovered, and the drawings, paintings, objects and creatures that he shows us.

Avery makes detailed pencil drawings of what he sees. What surprises us about the project as it unfolds is how strange it sounds in description, and how much less strange it often looks in the drawings.

Many of the drawings are beautifully wrought, and many of the creatures bizzarely engaging, but Avery lacks the writing and the thinking skills to give real coherence to his vision. It strives to be a satirical totality – while claiming, of course, that it is no such thing – but, finally, the whole project feels a bit serendipitous. The parts are greater than the whole.

To 8 November (020-7490 7373)