Hallo, again.
No answers yet, just two questions:
What is the earliest birth after 1837 (name, date, location if known, and parents' names) you have in your modern line?
Have you found the family on early censuses (1841 & 1851) - the first names of the parents, with the names, ages, and birthplaces of the children would be useful .
After 1837 we can find the mother's maiden name from the birth registration then check back for a marriage on parish registers.
Philip