Every society on Earth (and even some groups of animals) has adopted the same basic morality, independently of the twelve tribes of Israel. The nuances then grow as cultures and religions develop but morality came before religion, not the other way around.
The culture of Europe - and consequently Britain - had the teachings of the Catholic Church for the best part of eleven hundred years, from when Emperor Constantine converted the Roman Empire to Christianity to when Henry VIII broke away from the Catholic Church and Martin Luther pinned his note to the door.
During this time (most commonly known as 'The Dark Ages') the Bible was heavily influential in the politics of the European world. Biblical rulings like the right to own slaves, wives and daughters were property to be bartered for control of greater interests in business or politics and the persecution of those different from the norm, as dictated by the Holy Orders. These are Christian Values, just as much as Love Thy Neighbour as Thyself and Turning the Other Cheek. Atheists are often accused of cherry-picking from the Bible to make it look bad; Christians do exactly the same in the opposite direction. Jesus himself advocated hating family in Luke 14:26 and it's amazing how rarely that particular value isn't lauded by the Politicos.
Modern values actually have little to do with a Christian background and owe more to the Enlightenment; the Age of Reason. As reason became more frequently used as a tool for discovery things began to change into what we would consider modern morality. The fact that the Enlightenment happened in Europe is not a greatly significant notifier, it could have happened anywhere; it almost happened earlier in the Islamic countries of the Middle East, but was quelled by a sudden uprising of religious fundamentalism. Almost ironically, this sudden burst of insularity from the Muslim nations allowed the European Enlightenment to begin when the libraries left behind by the Islamic rulers of Spain were discovered.
Whenever the values were altered: freedom of slaves, equality of women, equality of different races and currently equality of different sexualities are the most notable, the churches were always a little late and often fought against the changes for several years until they bowed to the Zeitgeist. We can observe this happening today with the Christian opposition to gay rights, which mainly cites Leviticus. Just quickly contrast Leviticus 18:22, which is the most common argument against gay marriage and rights, with Leviticus 11. You never get many Christians adamantly insisting that Pork and Shellfish shouldn't be eaten, do you?
Cameron also claimed that the Bible supported the emancipation of women. Has he never read First Timothy Chapter 2? Here are some choice quotes:
11Let the woman learn in silence with all subjection.
12But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.
15Notwithstanding she shall be saved in childbearing...
So emancipation of women is basically an inferior position to men in all things, keep quiet bitch and get pregnant if you want a chance of seeing heaven. You can cherry-pick the Bible to tell whatever story you want, but it really invalidates the claim that it is a book of truth if you have to ignore specific parts of it to justify your point of view.
I could go on and on, but too much Bible bores most people, and most Christians even more so. The simple fact is that the values that Cameron is putting such an emphasis on are largely innate to all cultures or developed from the resistance to Christian rule. The only fair way to run a society is secular, religion has no place in politics. It's bad enough that we have a dozen bishops in the House of Lords for no reason other than that they are bishops in the Church of England.
Damn your Christian Values, Mr. Cameron. They are ancient, obsolete and unnecessary.
All Bible quotes are from the King James Version, which is to what Cameron referred.