It would seem that something has gone astray.
I would think that the best thing to do is back track.
I would start at the church and find out how the system works.
It's maybe that the docs go to the Registrars office in the town hall but until you ask you will not know.
When you discover what the church did you can follow the paper trail and see where the document is.
Maybe someone who married in a church can help. We had a garden wedding (5th anniversary today) so it was the mayor who married us. The next day we went to the registrars office and collected the notification which as I said we sent to the NSO. I think we collected the copy from NSO in about three weeks. I know we got it 'rushed through' as it normally takes longer.
Good Luck