If you look back through the Census returns, William Charlton and Elizabeth live continuously in the vicinity of Washington, at Harraton in1861 and Little Usworth in 1851 and 1841, always employed in agriculture although this is the heart of the Durham coalfield. I would suspect therefore that William was Little Usworth born and bred, and probably married Elizabeth there about 1830. Certainly their first child was born there. Satley where Elizabeth was born is a very rural place, not far from Healeyfield. She may have moved from there to find work as a farm servant at Usworth.
Hope this is of help.