Doodledog
Ours has a good system (sorry, I realise that's not what those with frustrating ones want to hear, but I mention it to show that it can be done). You go online and fill in a form with a brief description of the problem. You are guided through it with questions about how long it has been going on, what you want from the surgery (eg a consultation, a change of meds or whatever) whether it's getting worse and so on, so the triage team have enough information to work with. You can ask questions, too.
The forms are triaged twice a day and you get a call back (sometimes within the hour) to resolve it. You might get a call from a GP or nurse, or the receptionist might call to make an appointment, to tell you that your meds have been changed and will be at the chemist by tomorrow, or to pass on an answer to a question. Sometimes a GP will answer questions by text if they are straightforward. It is all very efficient.
As an example of the efficiency, Mr D had an odd-looking lump on his head, which he couldn't see, but I could. He kept saying it was fine, and put off getting it looked at, as men can be won't to do🙄. I took a photo and uploaded it to the system, said I was concerned and asked for advice, leaving his number so they didn't need to worry about speaking to me about him and breaking confidentiality. Within an hour he got a call asking him to come straight to the surgery, where a nurse practitioner said it was a basal cell carcinoma and prescribed some ointment to zap it. From my message to his applying the first lot of ointment took a couple of hours. You couldn't ask for better service.
It is so much better than the 8.00am scramble, but people still moan. The receptionist will fill in the form over the phone for anyone unable to do it themselves, but that that leads to complaints about having to tell the receptionist the nature of the problem, and people don't want to be triaged - they want to speak to a GP immediately, which is just not efficient and leads to longer queues for everyone else.
There are downsides around having to talk on the phone for patients who don't have privacy. You can't specify a time for a call back, but you can say when you are not available. Now that I am retired I don't need to do that, so can't say how well it works, but I assume they take working hours/commuting time etc into account.
I don't know whose responsibility it is to sort things out. Surgeries are businesses now, so the government can't impose systems (or can they?), but they could employ more GPs and other staff. My home town has nearly doubled in size since we moved here, but the number of GPs has stayed the same, and most of them are part-time. Things have declined over the past 15 years, so it can't be reversed by tomorrow, but I'd like to see a move towards a reasonable cap on the number of patients per GP in any surgery, and that would mean government involvement.
Many GP practices that used this system have to to restrict the hours of availability or, in the case of my GP practice, abandon it completely. People became rather too adept at using it and it generated so much extra work the practice couldn't cope. Having used it l can appreciate why, in order not to miss something crucial the submissions have to be checked regularly and quickly, GP surgeries became swamped. I hope it continues where you are, l thought it was an extremely useful tool but absolutely understood my GPs experience and frustration when it was explained.
