Seven centuries after the beginnings of classical civilisation in the Greece of Pericles and Socrates, an oriental superstition, consisting of an amalgam of dying and resurrecting god myths and myths about the impregnation of mortal maids by deities, captured the Roman Empire. Such was the beginning of Christianity. By the accident of its being the myth chosen by Constantine for his purposes, it plunged Europe into the dark ages for the next thousand years - scarcely any literature or philosophy, and the forgetting of the arts and crafts of classical civilisation (quite literally a return to daub and wattle because the engineering required for towers and domes was lost), before a struggle to escape the church's narrow ignorance and oppression saw the rebirth of classical learning, and its ethos of inquiry and autonomy, in the Renaissance.
Curiously, that thousand years with 'scarcely any literature or philosophy' includes Augustine, Boethius, Bede, Anselm, Abelard, Aquinas, Scotus, Roger Bacon, Buridan, Ockham, Dante, Chaucer, Langland, de Lorris, the Pearl Poet, El Cid, just to name a few. Be that as it may, one wonders whether in the sentence starting with "By the accident..." Grayling quite expects anyone to take him seriously. Did he somehow lose all his copies of history books written after the nineteenth century? And do we really need to be so breathlessly melodramatic -- by accident Constantine decides to issue an Edict of Toleration and whoosh! everything is doomed by that act? It's the Light Switch Theory of the Dark Ages: the lights were on when Socrates was around, but the Christians got together and convinced Constantine to switch them all off, and then made sure to keep them that way for a thousand years, when Renaissance humanists came around and flipped the switch again. It's really too bad for the pagans, too; things were just getting nice for them all when Christianity singlehandedly caused the Fall of Rome, and out of malicious obscurantism, no doubt.
In any case, I recommend reading the article; it's highly entertaining, like the preview of an apocalyptic movie. The complicated issues that are involved in the decay and deterioriation of the Roman Empire are not quite so striking, although certainly interesting in their own right. But you should also read some of the discussion at "Insight Scoop" here and here, where Grayling, or someone claiming to be him, jumps in to defend himself. If it is him, he defends himself very poorly. (Although, given what he's forced himself into defending, that's not really surprising.) In the context of the original article, the point was that the Pope and others are being irrational in demanding that the preamble of the European constitution have a mention of Europe's Christian traditions; as he puts it, this is "the plan of Angela Merkel and the Pope to recycle the old lie that the enslavement of the European mind by the absurdities of Christianity are foundational to what is in truth our secular, free-thinking, classically rooted inheritance." To support this conclusion he really does need the absurdly strong claims in his article; if, for instance, Christian culture contributed anything fundamental to the European legacy in the High Middle Ages, the argument collapses.
Of course, this wouldn't affect any other arguments for not introducing such phrases into the preamble, because they don't require anyone to make such blatantly untenable claims as Grayling's argument does.
UPDATE: Some of the limitations of this post are addressed here.