The Working Time Regulations were introduced in 1998 to give effect to the European Working Time Directive. They are a health and safety measure, primarily intended to ensure that working hours are limited, proper breaks are taken and that workers receive paid holidays. We do not know what impact Brexit will have on these regulations as the government will be free to repeal them if it chooses to do so. It is thought to be unlikely that there will be a wholesale repeal, but there may be some elements that are less popular with government and employers, and which may be subject to change.
