Disclaimer: I have not actually read this book so am being snide about it solely on the basis of the Guardian article (a risky proposition given the general level of understanding in newspaper book reviews).
The argument does however seem to be lacking in nuance. Of course there were atheists in Ancient Greece. The intellectual proclivities of the pre-Roman Conquest Greeks are well documented and in some cases philosophers even received the backing of powerful tyrants with one eye on their reputations. As Paul Kennedy has argued in his examination of the rise of Europe from the 16th century, political pluralism is always a boost to thinkers since they can easily migrate away from central authorities that clamp down on originality to freer polities.
Spotting the kernels of modern ideas is a common pursuit of scholars of the ancient world. Just do a google search on fascism and Plato or on the musings of Democritus on atomic structure. However, without an overarching theory of how these ideas developed towards the modern day they merely highlight the intellectual curiosity of the society that they arose in rather than telling us anything interesting about the ideas themselves.
Further there is no mention of the common tactic of accusing rivals of atheism as a form of propaganda. In large swathes of the world atheist has been a term of abuse and discrimination for centuries. Even in Ancient Greece we are informed that one of the charges brought against Socrates at his trial was impiety. Christian thinkers lined up after the fall of the Roman Empire to exclude atheists from their models of just societies and to condemn them to hell or purgatory for their lack of belief.
Thus it is hard to distinguish genuine atheism from its use as a term of opprobrium. Openly stated atheism could have lethal consequences in Christendom and much of the Arabic world. Searching for signs and double meanings hidden in the works of great writers who may have harboured doubts is liable to lead only to false pattern finding.
Long story short, atheism has almost certainly existed throughout world history but it is difficult to locate solid evidence for its continuity and influence outside of a few already well-documented examples.