Is no AC common in expensive hotels around the UK?

I find it usually depends on how old the building and hotel are and whether the hotel is an independent or part of a chain. You can stay in quite cheap but modern hotels and they'll have air con, as will more expensive and modern hotels. When you start looking at older buildings, it can be hit and miss and often comes down to whether the hotel is independent or part of a chain. Independent hotels in older buildings or converted buildings often don't have air conditioning, as it's not regularly needed in the UK. These older buildings are sometimes also listed (protected) buildings and you need extra permissions to make changes to the building, and there are much stricter rules about what you can and can't do with a listed building - and these often come with added expense too. Large chains in older buildings can benefit from their size, wealth and expertise to find ways around those rules or explore more expensive options for fitting air conditioning within the rules and restrictions - and that can apply to budget chains, luxury chains, and those in between.