Our online booking system is great, IME. You can book a named doctor (might have to wait longer if they're on leave, or only do part-time hours), or any female doctor or any male doctor. If you need a follow-up appointment, the GP can do it then and there from their surgery room.
You can also book the duty doctor, which is what you'd most likely choose for something urgent. Last time I had to do that (which was a couple of years back), I got an appointment the same day. I am fortunate enough not to know if that's typical or not. I've also not tried phoning for an urgent appointment (I love the online system - but I realise that not all patients will have internet access at home.)
You have to phone or call in person to book the nurse or phlebotomist. I was a bit miffed that I needed two separate appointments for a blood test and an inoculation on the same day, as at the practice I was previously registered at, the same nurse could do everything, but it's not actually a big deal - I just had different expectations because of what I'd had before.
I've also not had problems booking a couple of weeks ahead, for things like smear tests or blood pressure tests. It's also comparatively easy to get appointments first thing in the morning before work (I think the earliest is 08:15) - and there are a couple of days where they do evening appointments, though I've not tried to use those to know if it's easy to get a slot then. I think you can also get phone appointments, but again, that's not something I've tried.
When we arrive for an appointment, there's a touch screen system to check in, or you can talk to the receptionist. I think it helps that you don't have to take the receptionist's time if you don't need to, but that the option is there, if you're not confident with using the screen.
I can also manage repeat prescriptions online, or by writing, or by going to the surgery in person (via the receptionist) but I can't do those by phone.
However, I'm registered with a large, town-centre practice which has a number of GPs and a few nurses and thousands of patients. They've got (human) resources that previous practices I've been registered haven't had - more doctors, more nurses - so they can offer more appointments and longer opening hours. It's nothing like one practice I was registered with (I've moved towns quite a few times), where it was a single GP with a part time nurse. I can't see that smaller, more rural areas I've lived in would be able to run a practice like that in the same way.