Hi. If you were to write to these two churches:

1. Methodist Church, Gilsland, Carlisle, England.

2. Church of England, Gilsland Spa, Carlisle, England.

give the details of the ancestor, and they will check their church records and send you their findings.
Sorry, i can't remember which of the two is relevant, i have'nt looked into the Charlton side enough as yet, so have'nt been able to piece together anything other than Adam who is recorded as hung, and my grandfather Wallace Charlton who was one of a twin, who had several other brothers and sisters, Adam would have left a wife and children, from whom Wallace was decended. I believe there is still a Wallace family in Gilsland, but until i have time to look further into it, and find written confirmation, i don't know that i am related to them, but it is very likely as Gilsland is a small village. My Wallace Charlton died in the 60's. Many church records are not on official lists or internet sites, especially covering the 1800's, thankfully many church's keep good records. Let me know how you get on, i hope you find what you are looking for and that it is documented. They will reply to you.