I can definitely sympathise with this, although it isn't a UK wide problem. My local surgery (in a remote part of the country) consists of a couple of GPs who both know me personally and making an appointment involves a quick phone call (and chat to the receptionist who I also know personally).
When I was living in London it was completely different, getting an appointment involved phoning up the surgery the morning you wanted an appointment and hopping somebody hadn't done so before hand so they had space. There was no way to book an appointment in advance. It was easier to go to an NHS walk in centre, wait for a few hours, see a nurse, and have them refer me to A&E to see a doctor if need be.