I actually think we need to abandon the current model altogether, starting with the GP as the 1st point of contact.
Walk-in centres should be the default norm, and 111 should move to offering e-consult as well as phone. Huge chunks of the population see GP's for one off issues - minor illnesses, minor injuries. These can all be handled via the walk in model/111.
So all the kids with fevers, ear pain, minor cuts, utis, burns, scalds, twisted ankles etc would just go straight there. Set them up to be able to xray and do basic bloods, administer pain relief - and staff them properly. Staff for Psych as well as medical issues. Open 24/7.
This cuts down on stress on GP's, who can go back to managing patients who need overview or repeat, scheduled care, follow ups, etc - now chronic conditions are monitored properly, med reviews get done, people can get access for flare ups in asthma, eczema. More importantly, elderly people, who are likely to have multiple ongoing issues, can access someone with all that information who can support them when things wobble, rather it being left to deteriorate.
It would also drop strain on A&E as having access to help easily would mean a lot of people would go there when they were worried or unsure. Efficient GP access would reduce the amount of things deteriorating to urgent. Get the whole country used to having an annual review with bloods drawn prior - so many things are so much easier to treat if caught early.
A huge issue at the moment is that lots of people feel there's nowhere else to go but A&E. Combining this with 'Save the NHS' and GP's who aren't functioning effectively is dangerous.
I'm currently in hospital, and I spent Friday night sat on a chair in an A&E triage cubicle on an IV while I waited for a bed. It was eye-opening. Yes, a few timewasters, but far more who'd been 'sent' by GP's (including the chap with a dry throat) and a lot of worried people with moderate symptoms who all said the same thing - I'm not sure it really needs A&E but somethings wrong and I didn't know where else to go....