Every local studies library has a microfiche copy of the county's births, marriages and deaths, usually photographed from the parish reigster books. If an Anglican church, the actual books may well be with your county archives office and can be viewed - phone ahead to make an arrangement. However the Dissenters and Catholics have been less careful with their written records.
Beejay, the headstones only tell part of the story as plots are re-used over time, and infant neonatal births were often put into the nearest open grave alongside an often unrelated adult. Suicides, the executed and witches were often given unmarked graves, as were paupers. But after QE1's time all burials are recorded in the big parish book.