We were also fobbed off for about 2 years by GPs. We repeatedly pointed out developmental concerns starting around the age of 2, and GPs poo-poo'ed them with the whole "children develop at different rates" and "boys are often slower" nonsense.
Finally at 4yo, when he entered reception, within 3 days, we were given a meeting with the SENCO, who then coordinated everything for us, including getting us in touch with the school nurse who got us a referral to the paediatrician, as our GP refused to do this (long story, but suffice it to say that she is no longer our GP 
).
We had a tentative/working diagnosis within a few months, however, not a solid one until June his reception year, so roughly 9 months from it being picked up by school. He received his statement about the same time, although the school had put FT 1:1 in place right at the beginning of the school year when they realised he had SNs. He was almost 5yrs old at the time. We were quite lucky - we had a brilliant school that was very proactive and helpful. We have a paediatrician and OT who are very happy to be involved in his school progress (attending meetings, speaking to teachers if they have questions, visiting the school) and are equally happy to answer any and all questions we may have..even by email, so we don't have to hunt them down by phone. Everyone worked together to get his statement sorted quickly, and although his statement was a tad woolly, I wasn't worried, as his MS school went above and beyond what was required by the statement.
As far as support is concerned, we did have to fight the LA to get him into the local specialised school, but thankfully the paed, MS school, and OT were very supportive and the LA finally gave in after a tribunal date was set. The move to the SS has been wonderful - other than a few blips, he has been coping so much better with the smaller class sizes and activities/lessons geared to his level/attention span.
His paed meets with us every couple months - to check on his progress in general, how he is doing in school, how we are doing (and coping), to see if we have any concerns.
His OT meets with us whenever needed - she has (over the past 3 years) organised window locks on all our windows, a stable door for our kitchen for safety reasons, new fencing in our rear garden so he has a safe place to play, a Mac Major initially and recently a wheelchair (needed for when we go to busy/crowded places or places where a lot of walking is involved as he cannot cope with lots of people due to sensory issues, and while he is unbelievably hyperactive, cannot cope with long bouts of walking - possibly due to his dyspraxia). At this point, we email updates to her and if she (or we) have any concerns, then she arranges to meet with us - she will pop out to our house at the drop of a hat if we have any problems. She is an absolute star!
From an organisational standpoint, we haven't had any kind of support in that respect - no carer meetings or anything like that, although I think there might be some in the area (not sure). Most of our support has been down to extremely good paed and OT, and then his SS - they have carer meetings, and his class TA does support work, so we have her mobile number for if we ever need anyone to talk to about things. I guess what I mean is that we have had individual support - not NHS directed IYSWIM.
I will point out again that we have been extremely lucky thoughout this process - I know loads of people that are fighting for every little thing, and I feel so badly about that.