As DottyH has said it depends on the vicar. A catholic person can marry in a CofE church but often one of them has to be CofE and be/or have a contact and address on the local electoral register (to the church). If you know someone in the locality who is connecte the the church somehow - this would really help.
I assume it is a particularly attractive church so it really depends on the vicar and how popular/in demand the church is, but you might as well pick up the phone to the vicar of the chuch you want and ask them.