Prior to the Burial Laws Amendment Act 1880, parishioners could be buried in their parish churchyard only with a C of E ceremony; no other ceremony was permitted.
Following a row over the burial of an unbaptised two-year-old boy (from a Baptist family), at a churchyard just down the road from where I am now (which occupied the pages of the national pres for over a year and led to debates in Parliament) the law was changed so that anyone living within a parish now has the right to be buried within the parish churchyard (or burial ground) with a ceremony (or lack of one) appropriate to their own faith.
For anyone who wants to know the full history of the dispute, here's the link:
http://www.suffolkchurches.co.uk/akenham.htm