Not exactly. I mean, in the US, as far as I know in all/most jurisdictions you don't get a different tax rate depending on whether the property is vacant or not. But in many places you can get a sizable property tax deduction for historic designated properties, sometimes equal to 100% of the value of the structure. Note that in the UK "listed building" means the property is registered as being historically significant, https://en.wikipedia.org/wiki/Listed_building.

The exemption for vacant buildings only applies to listed buildings in the UK. E.g. https://www.clearway.co.uk/news/does-a-landlord-have-to-pay-... :

> If your commercial property belongs to one or more of the following categories, you’ll be eligible for an extended period of relief for business rates, provided that your property is fully empty and not in use:

...

> If your building is a listed building, you will only begin paying business rates once the property is occupied once again