This one is just a possibility but seem to be no other W&J marriages and possible his mother ended up in Gosport.
The Church of Latter Day Saints, International Genealogical Index, www.familysearch.org/, WILLIAM MITCHELL
Christening: 09 OCT 1806 Holy Trinity, Gosport, Hampshire
Father: WILLIAM MITCHELL
Messages: Extracted birth or christening record for the locality listed in the record.