Hi Dyspraxic Mum,
My son is very severely dyspraxic and we are in the state sector, I'm afraid it makes no difference. State schools are so constrained by resources, as is the NHS it is virtually impossible to get support without a fight.
I concur wholly with the guest who opted for private assessments, you have to prove your child has a difficulty before the LEA will even begin to listen. You could start with your GP but if you want to short-cut the process then you could to go the private route. If you have private health cover then you could ask your GP for a private referral to a paediatrician also, although you are perfectly entitled to an NHS referral this will take longer.
To organise an Educational Psychologist assessment try www.bps.org.uk
and for an Occupational Therapy assessment go to www.otip.co.uk
Make sure that you select a professional whose area of expertise includes dyspraxia.