I submitted a request for the name Mawdesley (as in the village/township) and then came across this forum using one of the several varient spellings!
I am a descendent of the Rev John Mawdesley b.Parbold 1754 and Curate of St. Cuthbert North Meols 1778-1814 (Lancashire Meals, not the Cheshire Mels). Speaking of spellings his father signed Mawdsley and his grandfather Mawdslay!
However I was also very intrigued by your Cave comment as amongst my Hesketh ancestors are Henry Hesketh of Simonswood who married Jane Cave at Walton in 1758. She was born Altcar 1737, the daughter of John Cave.
It would appear that not long afterwards they left Altcar and settled in Simonswood/Kirkby.
I know Caves aren't very numerous in Lancashire. Is this a branch of the family you mention? Dates etc so similar!