If neither party lives in the Registration District where a non-Anglican religious building is located then there are only very specific legal circumstances that will allow notice to be taken, and the ceremony to take place. These are only if :
there is no such religious building in the Registration District where either party resides AND the one stated for the ceremony is the closest geographically or;
at least one party has a current and on-going connection with the religious building where the ceremony is planned to take i.e. this is where they currently worship in person on a regular basis.
When giving notice the legal wording signed states which of the above applies, and the Perjury Act applies to any false declaration.
Unfortunately the fact that a building is in a Registration District where one party used to live and / or attend; where family have always had their ceremonies; where they know the incumbent well or used to sing in the choir; the incumbent has agreed to conduct the ceremony; the building is beautiful are not sufficient.
Where neither bullet point applies one / both parties could consider creating residency (minimum 9 days immediately before giving notice), with both parties giving notice on the same day (so the correct addresses can be used).