I, too, am trying to trace the Cave family from Wigan so had a little look at your Thomas Fairhurst Cave. According to the 1901 census he and Eliza had 2 more children, Alice (b1896 West Leigh, Lancs) and Norman (b1900 Kenton, Northumberland). According to other censuses his parents were Richard (b1851 Wigan) and Mary (1850 Manchester) and Richard's parents were Richard (1824 Haugh, Lancs) and Sarah (1824 Wigan). All these people ended up moving to the Durham area. Hope this is of some use to you.
I am trying to trace William Cave who was christened on 7 Oct 1820 in Wigan. His parents were John and Elizabeth. Can anyone help? Please.