A specialist also requires a referral in the UK. There are also much more medicines which are prescription-only than in the US.

That's why in practice we have all these (private) services to get easy GP appointments via phone, video or even online forms. While everyone knows those appointments can't realistically do any real medical work, they serve to give you prescriptions and referrals.

It's just a gatekeeping mechanism, that you can more easily bypass if you have money. The more you pay, the more they care about your user experience and how streamlined it is.