The world is going out with a whimper instead of a bang. The entire human race is pretty much sterile due to a nuclear accident. More large animals, except reindeer have suffered the same fate, while other small animals thrive to the point of being a threat. Civilization despairs and collapses, but after a period of barbarity, the apocalypse mellows into something more genteel if still dangerous. The eponymous hero, Algy Timberlane, and his wife Martha flee the village they have sheltered in for several years on a quest to find something better.
They wander through a chaotic world, encountering a host of eccentric characters including the 'physician' Dr Jingadangelow. Many deny the end of the world, putting their faith in ludicrous superstitions. Others turn the surviving remnants of past institutions. But the overall mood is one of resignation.
As can be guessed from this, Greybread's journey is more than physical. It's a quest for meaning in an increasingly meaningless world. In a sense, it is the opposite of most apocalyptic stories I've read. Most are really about a new beginning, a fresh start, but this one is about facing the end of everything. Ignoring that emotional journey reduces the novel into a series of random incidents.
The flashbacks to the immediate aftermath of the disaster, working chronologically backward, were of variable interest but ultimately fed into this theme. I found the account of the events leading to Algy's father's suicide particularly moving.
The ending, though subtly foreshadowed throughout the book, was a bit abrupt. (I can't say any more without spoiling it.) Nonetheless, I enjoyed it.