1851 census:
HO107/2361/419/4 - Sculcoates, Yorks
Francis Wilson Head 48 Cordwainer Journeyman b. Beverley
Jane " Wife 49 b. South Dalton
Emma " Dau 22 Servant (Domestic) b. Beverley
Ann E " Dau 13 Scholar b. Beverley
David Port Lodger 20 Cordwainer b. Beverley
Based on Francis' age and birthplace in this census, there is a good match on the IGI:
Francis Wilson, son of John Wilson and Mary, chr. 16 Oct 1803, St Mary & St Nicholas, Beverley.
One other child christened in the same church by John and Mary: Elizabeth (28 Jul 1805).
Also several children christened from 1806 onwards in St John & St Matin, Beverley - possibly by the same John and Mary Wilson, but as you say, it's a common name...
Rambler