Surgeries don't actually have to close for there to be a problem. There just needs to a fall in the number of GPs who have practices at any particular surgery.
Smaller surgeries can be inefficiently run. Our local surgery (serving a small town, of fewer than 5,000 people, plus some nearby villages) has 7 doctors working there, along with 5 nurses or nurse practitioners, 3 phlebotomists and 3 administrative staff. There are also 8 staff working in the dispensary which forms part of the centre itself, and an on-site (but separately run) pharmacy available (which always seems to have at least 6 staff present whenever I visit it). Surgeries with just one or two GPs, plus a receptionist, simply can't be as efficient.
Our surgery guarantees that same-day appointments will always be available as long as you don't mind which GP you get to see. (I arrived at 10am not long ago, seeking an appointment. The receptionist was extremely apologetic that there were no more morning slots left but she still found me an appointment at 4.50pm). Appointments can also be booked online.
Improvements in efficiency won't solve all of the problems that some people face when trying to see their GP but they'd certainly be a good start.