My (Midlothian) surgery also sticks the answerphone on during lunchtimes - drives me crazy. In addition, I went down last week to collect a prescription and the surgery was closed for Wed afternoon for staff training. There was a handwritten sign on the door saying so.
Emergency appointments are good. You phone (at 8.30 and hit redial for half an hour before finally getting through) but you/your child will be seen that day. I have been told that you can't have an emergency for the next day - it was a day when I had no car so couldn't get to the surgery and wanted an appt for the next morning. They told me to phone back the next morning. They've now introduced a triage system where the duty doctor calls you back, triages you over the phone and then either writes a prescription or tells you to come in at a specific time (same day). If you miss the call then you have to ring back, tell the receptionist and be re-entered into the phone call queue.
Routine appointments are terrible. You have to phone at 8.30 on two specific days of the week (think it's Wed and Thurs) when they 'release' appointments. You cannot make an appointment at any other time of day, even if you are in the surgery standing in front of them. When the office manager went on holiday recently no appointments were released until he came back! It's usually 2 weeks wait to see the duty doctor. I have requested my specific GP and been told that I have no specific GP because they don't do that (so how come she's named on my maternity records, then?), and if I want to see her anyway then it'll be 5 weeks, unless she happens to be the duty doctor. I complained about that and got a pretty crap non-reply from the practice manager showing no interest in making any changes.
You can, however, request a non-emergency phone call from the duty doctor. This will be at a specific given time eg next Tues at 11am. DH used that to be re-referred to the Eye Pavilion because despite having a rare eye condition and having been treated there in the past, because it was more than 3 years ago he had to get the GP to refer him again. GP had to Google said eye condition during the phone call. (Sorry, I know that's off-topic!)
Clinics: the midwives and HVs run their own clinics but the reception staff don't know anything about them, which is not helpful. The 6 week new baby check is organised as a clinic, eg all done on a Thurs morning, and if you want to be checked yourself post-birth than you have to make a separate appt, and therefore come back yet again, invariably with newborn baby. It's not set up from the patient's point of view at all, nor probably from the GP's - why not join those up and save a journey? Oh, and maternity notes aren't linked to standard medical notes - I have booked a flu jab when pg, arrived at surgery and the first thing the nurse asked me was why I needed a flu jab! I said 'because I'm pg' and took coat off to reveal 7 months pg bump, and the nurse apologised and said it wasn't in my notes. Why not?
Like most people have said, when you do see someone they are lovely (GP/nurse/midwife/HV) and take time and you never feel rushed.
Suggestions for improvement: look into Systems Thinking. Prof John Seddon is the UK leader in this and he specialises in sorting out bureaucratic messes like this in the public sector. I've worked with his company (Vanguard) and the methods he advocates really work. The surgery staff would be asked to analyse calls coming in and gather data on eg failure demand (where you have to call back multiple times to get the service you need), length of time for customer to get different types of appt, most popular requests (eg I want a GP appt/I want to see a specific GP etc) and whether they were fulfilled or not. Then the staff themselves suggest solutions. There's a lot more but this is already an epic post! But this could be trialled in one area and then rolled out if successful.