However my shared common ancestors with person B lived in Cumbria and my shared common ancestors with person C lived in Hertfordshire or Lincolnshire, so given the fact that back in the early 1800's the two families lived in completely different parts of the country make it very very very unlikely. It would be such a massive coincidence .
Britain was having a major war for the first 15 years of the 19th century. Young men were going here, there & everywhere, as soldiers, sailors or militia (last was equivalent of Home guard or Territorial Army).
War was followed by several years of economic depression and unemployment - more potential reasons for people to leave home.
England was the first country in the world to industrialise, another reason for movement of people.
England was first country to have railways, from 1830s. Engineers, builders and labourers to construct the lines & stations, some of the workforce coming from outside the area. Once opened they enabled faster transport. Canal network from previous century.
An important industry in Cumberland was mining. It attracted workers from far afield. When one type of mining or a mining region was declining and another type or region was expanding, miners would migrate.
Btw the name of the county is Cumberland. "Cumbria" didn't exist 200 years ago. Cumbria isn't a county. It's a local government unit created in 1974, comprising Cumberland, Westmorland, part of Lancashire and part of Yorkshire.
Are you sure your mothers and father's trees and other trees with matches are all correct?