The only problem with that is that a large proportion of the remaining small churches where build after QE1 and so are not theirs. Those that would qualify would need extensive restoration.
The large Cathedrals have been totally “redecorated” during the Civil war and would cost a fortune to restore to there former glory.
The monasteries would be an even greater problem as most are now part of the construction materials of the surrounding villages.
To be honest there are sufficient new Catholic Churches around the country, because of the break-up, built over the last two hundred years not to worry about the old crumbling expensive to maintain buildings.
However that could be an interesting situation to watch.
the sad thing is that some of the greatest places of English history are gone — the Abbey where St. Augustine came to Kent is now in ruins. I used to be a member of the British Historical society and it was a tragedy to me that so few visited it — even in the historical sense it is important to England.