If you go to Find My past and locate the Marriage, then follow the link to order a copy from the GRO Southport Lancashire, you will probably find the names of the respective fathers; and of witnesses who are often relatives.
This appears to be it, being in the expected Quarter-
Civil Registration event: Marriage Print Close Name: BEVAN,James Registration district: Merthyr Tydfil County: Glamorganshire Year of registration: 1838 Quarter of registration: Jan-Feb-Mar Spouse's last name: Not available before 1912 Volume no: 26 Page no: 453 MarriageFinder:James Bevan married one of the following people:
There was some duplication in references, hence the apparent selection of spouses!
The 1841 UK Census is also available on that site, so you may be able to find the family on it; and if the fathers have unusual first names, possibly their respective parents and any siblings.
You should also try to get copies of the respective Death Records of James and ann, presumably from the South Australian Archives, as these may also have the names of the parents, similar to Scottish Death Records, in the Statutory/Civil Registration series.