First of all this is William's baptism if you didn't already have it:
Name: William Swannell
Gender: Male
Baptism/Christening Date: 02 Feb 1817
Baptism/Christening Place: Stoke-Mandeville, Buckingham, England
Father's Name: Thomas Swannell
Mother's Name: Elizabeth
Indexing Project (Batch) Number: I04151-8
System Origin: England-EASy
Source Film Number: 1966917
Reference Number: pg 5 #38
I then found this marriage for Thomas and Elizabeth:
Thomas SWANNELL
Birth: About 1791 Of, Weston Turville, Buckingham, England
Marriages:
Spouse: Elizabeth COOPER
Marriage: 10 OCT 1816 Weston Turville, Buckingham, England
(the birth i assume is just taken from the same area of the marriage and they're not always accurate with the dates anyway).
however I also found this record...which looks a bit more ambiguous:
Thomas SWANNELL
Birth: About 1793 Of, Great Kimble, Buckingham, England
Marriages:
Spouse: Mrs. Elizabeth SWANNELL
Marriage: About 1818 Of, Great Kimble, Buckingham, England
this second record may just be a duplicate record...as it doesn't have any definite dates...or even names. either way if they are the correct records elizabeth may have been pregnant before marriage?
i'll try to see if I can find any other records to back this up though..as the records don't seem extremely reputable..
do you have any other information about thomas/elizabeth? including census records/deaths?