My understanding is that UK KYC basically don't specify exactly how to validate an individual's identity, only that the bank should do that (https://www.gov.uk/government/publications/identity-proofing...). It does suggest that a person's identity is "often someone’s name, date of birth and address", but it doesn't seem to mandate that.
I believe the requirement for banks to hold addresses is actually an AML requirement, and this only comes into effect for larger or riskier transactions.
In a sense, the requirement to have a "provable address" just to open a basic bank account becomes quite problematic when you consider there are people who don't have fixed addresses. Whats worse, you discover that most of the ways in which you can get a fixed address require you to have a bank account (e.g. renting a place to live). It's an entirely unnecessary chicken-and-egg scenario caused by the insistence of the older banks on collecting proof of address, which they didn't technically need to do.