Pooka, almost everyone on here has been told at least once, if not over and over, that their child won't get a statement - me included.
Your ds sounds very similar to mine at that age. We/he muddled through infants, raised our concerns regularly but were told the school saw no problems and we wasn't even on the SEN register. Unfortunately, he went to pieces when he entered juniors, even though it was the same school, same teachers, same rules etc. He couldn't cope with higher expectations on him in terms of self-reliance and organisation etc or the shift in social/peer group friendships and interaction.
Ds was referred to a Paediatrician by our GP when he was 7 and was diagnosed with Asperger's Syndrome when he was 8.
Apparently it's very common for high functioning children to end up with late diagnoses and the transition from infants to junior is one of the most common times for things to come to a head.
My ds is also has handwriting issues, but is in top set for everything, so doesn't have achievement issues, although we have eventually been able to get the school to admit that he still isn't achieving his potential despite being near the top of his year.
I applied for Statutory Assessment myself, in spite of what the SENCO and others etc told me about there being no chance of him getting a statement. He got Statutory Assessment and then a Statement on our first application, with no problem at all. The Ed Psych, Inclusion Team and Paediatrician all agreed what sort of support he needs to achieve his potential.
We still have issues with certain teachers refusing to agree that he has AS and needs additional support, even with his diagnosis, which has been confirmed many times over by different professionals. Plenty of staff at the school think I am the problem and that ds is fine, but they are wrong, not to mention extremely arrogant for thinking they know better than a team of 9 professionals.
The thing is, we now have a statutory document, the statement, that tells them they have no choice but to give him the support it sets out, so it doesn't matter what individual teachers might think, as the support has to be given regardless.
Personally, I would go to the GP now rather than waiting for an EP assessment. As Attila said, the EP can't diagnose, so their assessment will just be an extra step and delay in getting your ds a diagnosis (if appropriate) and the necessary support to cope with school. EP assessments have their place, but they aren't a substitute for a full assessment of his needs and issues. Our EP has been amazing, really good at getting to the root of ds's issues and needs and active in making sure the school meets them.
If it helps, my ds is now 10, in year 6. Since being diagnosed and getting appropriate support he has gone from an anxious, school-refuser who we very nearly pulled out of school to home-school, to actively getting upset if he has to have a day of due to illness. He loves school now, is doing much better socially and is happier all round.
I was very relieved to get the statement first time, as we were running short of time to make sure he got one before starting secondary and the process takes a very long time. We still have some problems with the school and getting the some aspects of the statement implemented is proving to be a bumpy ride, but it was still well worth fighting for.