We can book online for non-urgent things, and you can choose a named doctor or any female doctor or any male doctor. It's rare to get an appointment earlier than about 3 weeks ahead, if not more, and I don't think they show appointments more than two months ahead or so. If the GP wants to see you again in 2 weeks, that can be booked by him or her while you're there.
You have to ring to book the nurse or phlebotomist, who are not the same person, unlike in my previous surgery. I found this out when I turned up expecting the nurse to do BP, urine and bloods, but she couldn't do the blood tests. They were talking about putting this bit online, too, but I don't know if that's been done.
They used to have online booking for urgent, on the day cases which were just for the duty doctor, but I think now you can only phone. Last time I went, I had spoken to NHS Direct or whatever it's called currently, and they had already told the surgery I needed to be seen that day. Can't remember whether I phoned the normal number or a special one, but I didn't have to wait long, and I remember thinking, this is bloody brilliant service, compared with all I've read on threads like this one. I don't know if it's that efficient if you call without having had NHS Direct magically smooth the way.
Also, we have appointments from something like 07:15 to 19:00.
But - it's a large town centre practice with something like 15 GPs - that how they can offer that level of flexibility. (That's not why I chose it - it's about 8 minutes walk away.) My previous practice, in a small village, they had 3, and however you juggle rotas and so on, they just couldn't offer such early or late appointments or anything.) - it's a totally different logistical challenge.