I've been sent to A&E with my DS once when I didn't really need to go for lack of other appropriate resources.
I rang the non emergency help line but it was as though they washed their hands of us as soon as they heard a child was involved and sent us to A&E instead. I really think he could have been seen by a GP but it was out of hours.
I had a similar experience when I hurt my shoulder. It's a recurring problem which is very very painful when it happens, think an 8.5 on the pain scale if childbirth is 10. Typically it happened outside GPs hours. I rang the non emergency line again to find out where I could go and they panicked because the pain was in my left arm so they feared I was having a heart attack. The call took so long I'd have been dead if it was a heart attack in my opinion but hay ho.
They told me to go straight to A&E which I thought was ridiculous so I ended up crossing the entire city to go to the walk in centre, thinking this was more appropriate. I won't bother with that again, they only agreed to help me because I burst into tears and sent me to see the GP.
If there is a next time I will go straight to A&E and not mess about because at least then I will get to see a doctor even if I have to wait 6 hours.
Round my way, the system only works if you get ill before 8am on a Monday - Friday, otherwise you have no hope of a GPs appointment and A&E is your only other choice. Plus the only walk in centre is genuinely in the middle of fucking no where, Gods help you if you don't have car.