We fill in a form which gets reviewed. They then send a link with an option of times for in-person or phone appointments - last time I did it (about 5 months ago,) I was offered a range of slots from the next day until about 2 weeks later.
Before covid, you could phone or fill in an online form for a named GP, any make or any female GP or the duty GP. Then over covid it was phone only, which was crap.
When I've had a regular thing come up, e.g. bloods or smear, I get a text with a link to appointments, which is a definite improvement on having to phone for a nurse appointment only to be told they haven't released them for two weeks time yet.
If you can't do stuff online, you can still phone up, then basically the receptionist does the formfilling for you, and will call back with the list of appointments, so it's the same review system.
However, it's a large town centre practice, which also takes trainee GPs, so I think they have more resources and flexibility than e.g. my previous village practice.