I agree with hunting though Parish records. I came across a set of twins born of Moses Bate & Mary Ann Smith Bate on this site. They were born in 1846 & died on the same day - five weeks later.

After I put them into my 'tree' the information re: them came up on a 'hint' on ancestry. Sad to find them, but thrilled being able to get the information from a Parish Records search on this wonderful site!

It may take some effort on your part but it will be well worth it!