It seems to me that the classical cannon of literature, meaning dramas (plays), poetry and, latterly, novels, are more founded on Classical literature and Classical allusion than Biblical literature and allusion. Granted, many themes have come from the Bible, yet recall that the clergy were the only ones to have access to Biblical literature and to writing their own literature (miracle and Mystery plays) until after Martin Luther's time. Recall further that Biblical literature would not have had any impact on Greek or Latin classical literature because, quite simply, those earliest, founding writers worshipped pagan Gods. Therefore it seems to me that Classical literature has the greatest impact and influence on and is most important to English literature.
I think that you have to know both the Bible and the classics in order to understand allusions in modern literature. I would say that both are alluded to in the literary cannon, often in the same work. For modern writers, the Bible might be more common for some and the classics for others. If you are reading and you notice a lot of references you don’t understand, the classics or the Bible are a good place to start. I don’t really think it’s fair to pit them against each other. You do really need a background in each.
I agree with the post above. Both backgrounds are historically relevant and significant to English literature, but I would say that England's long-standing history with the Christian church and beliefs has more of an overall influence than classical literature. Classical literature definitely has been influential, but not to the extent that Christianity has, especially in terms of affecting the morals, ideology, faith, beliefs of the authors and poets who then translate those beliefs and morals into lasting written works.
This is a controversial statement, because English literature presupposes both the Bible and classical literature. However, if I had to pick one, I would say that the Biblical background is more important. Let me give you a few reasons why.
First, from the point of view of worldviews, English literature was started by people whose common sense view of the world was filled with the Bible, whether they were religious or not. In other words, Europe was shaped by Christianity. So even if an author revolted from Christianity, it was based on a biblical world view. We can say that it was a reaction against Christianity.
Second, as important as the classical world was for Europe, Christianity in time took over and more importantly, classical literature was mediated through the lens of Christianity. For this reason also, Christianity is essential as a background to English literature.
In light of these points, we would do to remember the importance of Christianity in reading English literature.