David Cameron was wrong, Britain is more accurately described as a post-Christian
The influence of Christianity has enormously waned. The Church of England is a lukewarm and vestigial institution.
The only sense in which Cameron was right would be "nominally Christian", Christian in name only. That would be misleading, however, since having moved on it's more accurately called post-Christian, retaining a vestige of its Christian past.
Britain has Christians, Muslims, Neopagans, Buddhists, atheists, agnostics, and many others.
The other sense he was wrong is in implying that the moral foundation of British culture (as with other Western societies) is rooted primarily in Christianity and the Bible. That neglects the strong cultural influence of Classical Greek philosophy and ethics - Socrates, Plato, Aristotle, Epicurus, Zeno of Citium, and others, not one of them Christian. Not to mention the Enlightenment, in more recent times.
Not to mention, this famous Englishman, enshrined on British currency, wasn't exactly a defender of the faith: