There is a good survival rate of Bible Christian baptismal registers, which will have been deposited in the county record offices. The problem, common to all branches of Methodism, is that you will probably have to work out to which Circuit your ancestors’ chapel belonged, but as Bible Christian Circuits were quite small you will probably have a good chance of working this out. Go to the National Archives catalogue at http://discovery.nationalarchives.gov.uk/ and use “Bible Christian” and the place in which you are interested, or the county, to find out where the original registers are held.
It was not legal to marry anywhere but a parish church until 1857, and most Bible Christian chapels did not register for marriages until 1898, so it is unlikely you will find any Bible Christian marriage registers. In any case, the certificates obtainable from the General Registry Office, or local Registry offices will tell you where the marriage took place (e.g. in the chapel).
There are few surviving chapel burial registers. The one for Lake Chapel, Shebbear has been transcribed and is available at http://genuki.cs.ncl.ac.uk/DEV/Shebbear/BibleChristians/AppendixC.html
The attached document compiled by Philip Thornborow explains and lists Bible Christian baptismal registers with a number of online links. Cornish registers have been transcribed by Cornwall Online Parish Clerks whilst a number of other baptismal registers have been transcribed by local family history societies, either online or in print and are listed here.
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