The Tides of Time — John Brunner

First there was the end.

After weeks of running from pursuers, Gene and Stacy finally found refuge on an isolated island.

But around them the island changed - and so did they.

Each time they awoke from sleep, they lived a different life in a different time. And the farther back they went, the more they lost their anchor to their own world. When at last they were found, the people they had become no longer recognised their pursuers.

And that was the beginning.