I'd guess you're mainly referring to the Elizabethan Act of Uniformity and related laws from the same period which set out the church laws and their connection to the state.
Some of the provisions in the Act of Uniformity were repealed or modified in 1650 by the Rump Parliament and Cromwell. They were replaced by other restrictive laws, such as the Blasphemy Act.
In 1689, The Act of Toleration repealed most of the provisions of earlier acts and provided a measure of religious freedom for most Protestant denominations although Catholics and others were still effectively outlawed or restricted. These ongoing restrictions became an important reason for people to immigrate to the American colonies.
Over the centuries, parts of these religious laws were repealed or modified as suited the contemporaneous political events. For example, the Roman Catholic Relief Acts in 1791 and 1829 were intended to help deal with the political situation in Ireland and to better handle political events in Europe. This continues today, most recently with provisions in the 2010 Equality Act.