No, it's not the same for the rest of the country, and to be perfectly honest if I was you I wouldn't be sitting at home fuming about it, I'd be down to the surgery in person kicking up a stink about it demanding an appointment.
I can ring my surgery in the morning and get an appointment with a gp that same day if necessary. I can ring and make an advance appointment for the following week too. I can also ring in the morning and get an appointment with my own gp the same day if it's a day she's on duty. I can ring and make a telephone appointment the same day too.
My practice is a huge practice which has eight doctors plus locums, and trainees as its also a teaching practice.
Either I'm very lucky or you're particularly unlucky Jenny, but there is no way I would accept what you've been offered.