There's a thread about this in Primary Education - www.mumsnet.com/Talk/primary/2602414-education-psychologist?msgid=60188979#60188979. A poster called SupplySam has come up with a gem of a post implying that all independent EPs are charlatans, which includes this:
"If you want a report for information for the school, your child has to be referred through the school. If they won't refer, then a referral is probably not necessary."
If only. If anyone cares to post on that thread with their experience of relying on schools to organise EP reports, do join in.