DD was referred to the Ed Psych at school at the end of yr 4/start of yr 5. I'm trying to remember exactly how the process went. IIRC first the EP met dd briefly while she was in school seeing other pupils. Then a fortnight or so later she had a session with dd and a session with us (asking background questions eg did she meet development milestones as expected when younger, how did problems at school affect her at home, things like that).
Then she had another session with dd and later met us again to give feedback (I think the HT who was also SENCO was in that meeting?), perhaps a month further on, something like that. Then a final check in with dd & her teacher to see how the strategies put in place were working later that term.
She had a brief session with dd a few weeks ago to see how things were going (so roughly a year after all this took place) and we were invited in again for some final feedback which also in our case included some suggestions on helping dd with her secondary transfer.
I think we got a letter after the first meeting quite quickly, but then after the second meeting she'd mentioned putting things in writing for us but didn't, though dd did get a letter herself confirming the strategies that the EP had suggested she/her teacher could try out.
We emailed and she then sent us a copy of her report to school (so results of the various VR/NVR tests as well as other stuff).
HTH!