There's plenty of secular ethical philosophies, many of them don't have a set of moral laws. Consequentialism, Utilitarianism, Humanism, Deontology, Hedonism, and Objectivism are a few. Some people don't believe in moral truths, there are different philosophies that imply this, I think the more general term is moral skepticism.
You don't need to believe or subscribe to a religion to be moral. Some animals including humans are capable of moral behavior. and living in a community, without religion. Societies exist without everyone subscribing to the same moral code. In issues where morals might be in conflict, they're ultimately solved politically. Some moral concepts like the golden rule seem to arise commonly, suggesting they're independent of religion. Evolutionary psychology is trying to explain why we seem to have innate morals.
If you take Christianity as an example, as a source of morals, it doesn't seem a great one. These morals have quite visibly changed over time independent of revelation. Looking at the Bible, not many people follow these rules in modern societies, but I find some of its suggestions to be abhorrent. Are the Ten Commandments a great set of moral principles? Not at all. They're not detailed or specific, a lot of time is spent on believing in God, Sabbath, false idols that to me have nothing to do with morals, they appear to represent women as objects owned by men along with donkeys, and tacit approval of slavery. They're a really bad attempt at a moral code, to modern society they're not moral at all. They wouldn't be a good base for law at all, they can be interpreted in numerous ways.