Update - Actons of Blackrod Parish, Lancashire.
Okay, the story so far.
Thomas Acton (b. circa 1775) - the son of William Acton and Mary Farrington (?) - was married twice, firstly to Mary Collison who bore him at least three children and died aged 38 (in 1815), then to Nancy Bean with whom he had at least four children; Matty/Martha, Mary, Robert & Fanny. Mary died at the age of 12, but Matty had two sons (Thomas and John) who both carried on the line. (my family are decended from John's daughter Ellen)
Robert married Ann and moved to Adlington, a few miles away, with his wife and son William. They both died there, although Robert is mentioned in the Parish burial registers for Blackrod's St.Katharine's Church.
William married (Isabella?) and had a son (Thomas - born Adlington in 1880)
Fanny was an unmarried mother like her elder sister Matty (Martha) her son Ralph became a blacksmith and married Ellen Speak. They had at least five children, two of whom (Grace and Lily - born 1889) were apparently twins. Fanny also had a daughter named Nancy and (possibly) a son, William.