Even in highly secular societies, religion and other belief systems play a huge part in shaping people's lives. In many parts of the world, there is no distinction between religion and other areas of life—religion is an overriding and unifying force for how people move throughout the world. In Amish (also called Pennsylvania Dutch) communities, every aspect of life exists in reference to religion. The clothes people wear, the food they eat, and even the hobbies they take up are all shaped by what is considered appropriate in this ethno-religious sect.
That might sound pretty extreme, but let's take a moment to consider some of the major world religions. In Judaism, Christianity, and Islam, there are rules about what kind of foods people should eat and when, how to care for one's body, what kinds of clothing are appropriate, when work is to be done, and what kind of gender, age, and familial roles are to be fulfilled. In secular societies like the United Kingdom, people may adhere loosely or very strictly to their religious duties while still maintaining their religious identity. For example, not all Christians fast during Lent, and some Jewish people do not keep kosher.
That being said, some aspects of religious belief systems are more influential in a society than others. Most cultures of the world today observe the Gregorian calendar (which was introduced by Pope Gregory XIII) and observe the weekend. The cultural practice of not working on the weekend is drawn from Jewish and Christian religious traditions, which forbid working on the Sabbath. For the Jewish community, the Sabbath is held on Saturday; for Christians, on Sunday. Regardless of whether someone is or is not Christian or Jewish, most people today abstain from work on the week-end or consider it a time for leisure.
I'd like to make a distinction between religion and other belief systems. Religious beliefs aren't the only worldviews which shape culture—scientific belief systems and ethical belief systems are also significant. Scientific belief systems outline how to go about answering questions we have about the world and what answers have already been uncovered. For example, I believe rain is the result of condensation of water vapor and occurs as part of the water cycle. I believe this because scientific study provides evidence for it. Alternate answers have been proposed, such as that rain is a gift from a deity, but I feel the rigorous investigation and testing of science is more plausible. Most people in my culture agree that rain is the result of natural temperature and weather patterns, so we do not adjust our behaviors in any way to try and please the deity in charge of rain.
Ethical belief systems help us to understand and investigate which behaviors are ethical, moral, or good, and which are not. In some cultures, the ethical belief system dictates it is immoral to eat meat. This may be tied to a religious belief (as in Hinduism and Buddhism) or may exist regardless of a religious narrative. Ethical belief systems also guide us in our personal behaviors and relationships. Having a culturally taught system of ethics helps prevent injurious action and may prescribe appropriate penance. For example, in my culture, it is considered unethical to steal. In exceptional circumstances, it may be excusable. For example, is it more ethical for an impoverished mother to let her child starve or to steal food so they can eat? In my culture, it would be excusable for the mother to steal to feed her child, but my government has set up programs designed to prevent this dilemma from occurring in the first place. The overriding ethic here is that all people should have enough food to eat. This may be phrased in terms of religion or scientific value, but it is also a standalone matter of ethical value.