Transit — Edmund Cooper

It lay in the grass, tiny and white and burning. He stooped, put out his fingers. And then there was nothing. Nothing but darkness and oblivion. A split second demolition of the world of Richard Avery.
From a damp February afternoon in Kensington Gardens, Avery is precipitated into a world of apparent unreason. A world in which his intelligence is tested by computers, and which he is finally left on a strange tropical island with three companions, and a strong human desire to survive.

But then the mystery deepens: for there are two moons in the sky, and the rabbits have six legs, and there is a physically satisfying reason for the entire situation.