Privacy

First: VPNs are also used by businesses to allow access for remote workers and sites to the company's internal network. In fact, this used to be their most common use and maybe still is.

Second: what's stopping a foreign VPN provider from offering a VPN service to UK customers without forcing them to identify themselves? If such a company doesn't have UK owners, workers or assets all that the UK authorities could do to enforce a court judgement against them is force British ISPs to block the IP addresses of that provider's VPN servers, which would easilly turn into an a whack-a-mole situation, more so if VPS providers started selling "easy personal VPN server setup" facilities for their virtual personal servers which would make that an insane whack-a-mole situation.

The "VPN server on a rented VPS" situation could easilly turn trully insane to try to block - there are A LOT of VPS providers outside the UK selling pretty cheap services good enough to run a personal VPN server and even without the VPS providers leaning into it by providing an out-of-the-box option (and merelly supporting Turnkey Linux images means having two linux server images that work as VPN servers out of the box), step by step instruction of how to make it work with normal server distros will soon emerge and become common knowledge amongst Britons with even just basic technical skills.

In summary, the UK is a pigmy trying to look like a giant when it comes to how much their laws will influence foreign VPN providers in a market which is pretty competitive and were there is no one dominant market participant which can be pressured to have an implementation "for UK customers only", and even if they found a way to enforce that law on all foreign VPN providers, that's not enough at a technical level to stop people altogether from having access to no-authentication VPN service since anybody can rent a VPS anywhere and run their own VPN server in it.