Actually the Church of England is government (and taxpayer) funded. Money for building repairs comes straight out of the Budget as demonstrated here:
https://www.churchofengland.org/med...-£40-million-for-church-building-repairs.aspx
This money is pooled from taxpayer's monies from all parts of the UK - even ones where the Church of England doesn't have any significant presence.
There's also chancel repair liability where ordinary citizens are expected to stump up amounts totalling tens of thousands of pounds in order to fix nearby Anglican properties; even if they're not Anglican. This liability can be placed on them even if no mention of it was made in the deed to their property.
There is a distinction between funds given to churches by the various heritage funds for the up keep of public buildings of various sorts And church funds for religious purposes. The Church of England is in the unfortunate position of having a vast number of heritage buildings that it must upkeep and may not sell or dispose of.
It must allow anyone of any faith or none to enter its churches as of right.
Such buildings that are not listed, it can get permission to close and dispose of.
In recent years it has closed many redundant churches.
However there are usually covenants in place as to what must happen to them.
Likewise, as the established church, they must look to the spiritual needs of the entire population , not just Anglicans. They are encompassed by laws as to what they may and may not do.
To day with falling membership they are in a most unenviable financial position.
The Chancel repair Liability is no longer available. there are no church taxes in the UK.
The various Heritage funds derive money from many sources including the government and lottery funds and various established charities set up for this purpose.. Any owner of heritage property can apply for funding for essential repairs. In the case of a church it is always "match funding" and is never more then 50% of the cost.
A down side of applying for such funding is that all repairs must be carried out to particularly onerous standards such as the use of matching original stone and lime mortar and plaster. Wood is usually specified as English oak, and metal work gutters and down pipes as cast iron matching the original. design.
There is no economy option.