Charles Avery, artist: 'I was kicked out of Central St Martins because I wanted to draw and draw'

Charles Avery recently moved into his portion of a new low-rise building in Homerton, east London, sharing two floors with three other artists. He greets me, warning in advance that his studio is "a work in progress".

When they moved in last January it was a concrete shell. They have since put in a rudimentary flight of stairs and today his assistant is busy laying floorboards in what will eventually be an open-plan studio flooded with light. Under the stairs, there is a beautiful set of storage drawers that his assistant designed and constructed to organise all his studio detritus.

Avery is back in London from the island of Mull, off the west coast of Scotland, where he was born in 1973. He spends about a third of the year there with his wife and three daughters. "At least I have a studio," he says of his young brood. "As the house is destroyed."

Avery's mother was an artist and his father an architect but they split up when he was young and he moved to Edinburgh.

I ask him if Mull is his creative inspiration but he says that he gets no ideas when he is there because he is so immersed in the beauty of his surroundings. "Looking is inspiring. Why would you do anything but be in it?"

As a student, he was kicked out of Central Saint Martins. Without going into specifics he says it was down to his attitude. "I had strong ideas and I wanted to draw and draw and draw. The tutors said, 'We want you to stop drawing because you know how to draw.' Drawing is not a masterable art."

Since 2003 Avery has been focusing on The Islanders, his long-term project devoted to an imaginary world that "represents the world of all ideas". Drawing is how Avery works out how his characters come to life and evolve. He shows me a recent drawing of a Murpish, a creature that lives in water and that the inhabitants harpoon and eat. It looks creepily human, hanging from the islander's hand. "I do not dream of the characters but they do talk to me during that intimate process of working on a piece of paper, drawing from the imagination".

Avery's dream is to create a sculpture park on Mull encapsulating his imaginary world. He has already managed to get planning permission to construct a jetty. His recent commission by the Edinburgh Arts Festival, which stood in Edinburgh's Waverley station with its colourful plastic limbs, has now been transplanted to east London – a small piece of Avery's magical world in the city.

Charles Avery: Parasolstice-Winter Light 2015 is at London's Parasol Unit until 6 December (www.parasol-unit.org)