The Eighth Dimension by Colin Blackburn

A mysterious ring of light appears in Kevin’s bedroom and voices urge him to come through the ring. He does so and appears in another world where he is mistaken for a god. He manages to help the people there but makes an enemy of the chief priest, Harlan. Harlan makes an attempt to seize power but is foiled and flees through the ring of light, taking all the jewel stones with him. Kevin needs the jewel stones to make the apparatus that generates the ring to work, allowing him to return to his own world. He is forced to follow Harlan into yet another world, where men are farmed for food by creatures that have been created from bionic experiments on cats. The world is blighted by atomic war and germ warfare that has killed all the animals, making man the only food source for the cats. Can Kevin retrieve the stones he needs and help win the war?