My pet crank proposal for this would be that listed buildings should require somebody from the public to pay to keep them on the list. Nowhere near the full cost, something in the region of £100.

Add a crowdfunding frontend. Put the sponsor's name on the website next to the building. Have a little thing promoting all the unsponsored buildings. Run a lottery which pays back some of the collected fees to privately-held listed building owners to help pay for upkeep.

But if nobody cares enough to reach into their pocket and spend the equivalent of a mildly expensive restaurant dinner on keeping this building listed? Maybe it's not actually important or significant at all. Fewer, better-maintained historic buildings, rather than just having them with the owner quietly waiting for them to burn down so something useful can be built.