If every website needed verification, why not simply move the verification to the device or ISP level? This seems like an authoritative move to track users across websites, and another good reason to keep using a VPN.
Certainly a terrifying amount of responsibility and upkeep for each individual website. If the UK wishes to establish this and not want it to lead to an insane amount of privacy leaks, it should consider developing a technology that makes it work in a privacy-respecting way, like the European Age Verification Solution [0]'s Zero-Knowledge Proofs.