Not that this helps finding Mary's maiden name - what about naming patterns of their children?
Is this John Barrington Day and his family?
Civil parish
Stoke St Gregory
1841 Piece 941 Folio10Page 15
James Day 45
Ellen Day 45
John Day 3George Day 5
1851 Piece 1922 Folio 320 Page 31
Stoke Gregory
James Day 57 Farmer of 30 Acres
Elinor Day 57
George Day 16 Farmers son employed on farm
John Day 14 Stoke, Somerset. DittoJames Smith servant 16
Is this the above George found in non-conformist records
George Gill DAYBirth 10 Jul 1835 St Gregory, Somerset,
Father
James DAY Mother
Mary dau of Samuel
BARRINGTONGeorge Gill DAY minor, father James both Farmers
married 16 Apr 1855 Charles the Martyr
Sophia WOOD, father William
I see on the 1911 Canadian census that she says she immigrated in 1863 and is Presbyterian.
I wonder if she'll be on a non-conformist baptism register?
Potentially Mary ? should be on the UK census 1851 & 1861
This is the closest I could find to
18th May 1842 birth date given for Mary DAY
BUT she has a middle name and a different place of birth
Mary Jane STREET 9 weeks
Father: John Street Mother: Martha Ann
Baptism
15 May 1842 Swindon, Wiltshire
There is this non-conformist entry with the exact dob but she was born in Lancashire - so doubtful if this is her
Mary SPENCER Birth
18 May 1842 Higham, Lancaster
Event Type: Birth
Father: John Spencer Mother: Mary Hendal