Spouse is probably Ann Lemon.
The Birth, marriage and children's birth locations are diverse. Surrey, Devon and Bristol. In spite of this there is a good match with names within the date range.
Sources
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J7KP-YXH : 8 March 2018, Ann Wilcox, ); citing item 3, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,595,986.
"England, Devon, Parish Registers, 1538-1912," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KC9K-6Z9 : 4 November 2017), Arthur Wilcox and Ann Lemon, 1805, Marriage; from "Church of England parish registers 1538-1911," database and images, findmypast (http://www.findmypast.com : n.d.); citing Devon, archive reference , images provided by FamilySearch International.
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JQ2H-Y6X : 11 February 2018, Arthur Wilcox, 18 Dec 1782); citing , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 307,706.
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