They are also both R.C.. Perhaps they were married hurriedly by a priest in a church, but there was no registrar present, so there would be no listing of the marriage on the GRO (that is the civil register).
The church is responsible for registering marriages that take place in their jurisdiction, copies are sent to the regional registration office which then sends them to GRO. In these cases the person who performs the marriage has the role of registrar.

It might be that there was no marriage because the lass in question was already married, which might explain why you cannot find a birth for her with the name she has presented as her maiden name. If they were R C then divorce was out of the question.