Maybe that’s specific to UK? I’ve never had to upload ID at any of the general domain registrars but am not in the UK. Maybe you’re looking for a registrar that doesn’t do that for UK residents, specifically. (or you might need to use a VPN or something, dunno)

Privacy aside most people tend to buy a domain at the cheapest registrar (keeping in mind whether to renew at that registrar later or transfer out to a new one when the time comes). There are domain registrar sites people use for comparison, been a bit since I’ve needed to shop around but sites like tld-list.com can be helpful. You could try doing a lookup there and work your way down the list until you find one you like.

Or if you’re really set on looking for a service that actually advertises no KYC then looking through this list may help kycnot.me/?categories=domains (njalla is one of the listed ones there as someone else mentioned).