Anthony Walton
born April 1831–April 1832
  in Co. Durham
died very roughly 1901

1841 census: (as Holms) living in Waldridge with grandmother, uncles, and cousin. Age is 9, born in county.

My first thought was that he and the 'Francis' shown in the same household were children of Mary Holmes as the 1841 census doesn't show relationships, but according to Amanda Cozens, he was the son of Martha Walton, née Holmes. Amanda says that he once ran the High Force Inn in Middleton-in-Teesdale.