"Particular search, traced or untraced £5.00"
I would go for the marriage(Unless you are prepared to wait 2 years for SP catch up)
I think you are fairly certain it is the correct certificate and it should give you both sets of parents
It might be a good idea to make up a sheet of paper before you go to the Registrars
It's easy to mix up details or miss something important
Example -
Date , where married , according to the Church of ?
Groom , Occupation , Age , Address , Father(Occupation) , Mother(Maiden Surname) (Are Deceased ?)
Bridegroom , etc.
Witnesses ?
Good luck on your search

ev