Marriage of Robert Grice and Ann Harrison 1831 and finding her birth details?

[Mills1960]

Robert and Ann married June 9, 1831 in Winteringham, Yorkshire. I am trying to find proof of who the parents were of Ann and her actual birth date. I have found a number of subsequent records that all differ as to when Ann was probably born.
Census 1841, aged 35
Census 1851, aged 47 (born Birstall/Birdsall?)
Immigration 1855 aboard "Ocean Chief" Jan-Mar 1855, aged 48
Died 14 Jan 1878 in Richmond Tasmania age 74
A number of family trees show Ann as born Jan 28, 1803 in Birdsall to Christopher Harrison but I can't verify that.
Is it possible to apply for a copy of the marriage certificate and would that show her parents names

[Kay99]

The church marriage record is on FindMyPast pre the introduction of civil records in 1837.  No fathers are listed and both partners are described as being single and of the parish.   Witnesses  James Young and ??   The groom signed his name

Kay

[Pinetree]

Hi Mills1960

Unfortunately Parish Registers from this period do not give father’s names.

From the Register the marriage actually took place on 9 June 1832. Both of this parish, bach and spin,
Robert signed, Ann made her mark, witnesses James Young and Jn Spanton.

Pinetree

Crossed with Kay