The Gloucestershire Registration Service, in conjunction with the Glos Family History Society, have indexed many of the BMDs for Gloucestershire and this can be searched here:
http://ww3.gloucestershire.gov.uk/bmd/
Searching this for Elizabeth's birth, it shows her mother's maiden name was Stroud. [entry 9 in the first register!]
When I was in the Record Office, I had a look for her parents' marriage for you and found this entry in the parish register for St Marys, Charlton Kings:
25 Dec 1830 by banns
Henry Morgan, bachelor, of the parish and Maria Stroud, spinster, of the parish. Both made their mark. Witnesses: George [X] Stroud, Mary Stroud.