Mary's birthplace was Watlington, Oxfordshire (about 2 miles from Shirburn) so I'm not too optimistic about that London marriage. Her age was 48 in the 1851 census but unfortunately there was a flood of Marys born in October 1802 in Watlington:
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J7S5-5QX : accessed 4 April 2016), Mary Adams, 10 Oct 1802; citing WATLINGTON,OXFORD,ENGLAND, reference ; FHL microfilm 887,489
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J7S5-5FC : accessed 4 April 2016), Mary Bracey, 08 Oct 1802; citing WATLINGTON,OXFORD,ENGLAND, reference ; FHL microfilm 887,489
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JMTF-6WL : accessed 4 April 2016), Mary Gum, 23 Oct 1802; citing WATLINGTON,OXFORD,ENGLAND, reference ; FHL microfilm 887,489
And there are a couple of Mary Anns too.