The marriage entry has been transcribed twice by FamilySearch so I doubt there would be additional information in the Parish Register.
Unless non-conformist or Catholic, you will rarely see the parents names mentioned in the marraige record in the Parish Register until later in the century.
Groom's Name: Abel Taylor
Groom's Birth Date:
Groom's Birthplace:
Groom's Age:
Bride's Name: Ann Hall
Bride's Birth Date:
Bride's Birthplace:
Bride's Age:
Marriage Date: 04 Sep 1826
Marriage Place: St. Philip'S Cathedral, Birmingham, Warwick, England
Groom's Father's Name:
Groom's Mother's Name:
Bride's Father's Name:
Bride's Mother's Name:
Groom's Race:
Groom's Marital Status:
Groom's Previous Wife's Name:
Bride's Race:
Bride's Marital Status:
Bride's Previous Husband's Name:
Indexing Project (Batch) Number: I02901-6
System Origin: England-EASy
Source Film Number: 813728
Reference Number: 198
Groom's Name: Abel Taylor
Groom's Birth Date:
Groom's Birthplace:
Groom's Age:
Bride's Name: Ann Hall
Bride's Birth Date:
Bride's Birthplace:
Bride's Age:
Marriage Date: 04 Sep 1826
Marriage Place: Saint Phillips,Birmingham,Warwick,England
Groom's Father's Name:
Groom's Mother's Name:
Bride's Father's Name:
Bride's Mother's Name:
Groom's Race:
Groom's Marital Status:
Groom's Previous Wife's Name:
Bride's Race:
Bride's Marital Status:
Bride's Previous Husband's Name:
Indexing Project (Batch) Number: M04179-1
System Origin: England-ODM
Source Film Number: 814245
Reference Number:
You can contact the Online Parish Clerks to see if they can assist.
http://www.hunimex.com/warwick/opc/opc.html