Please right away write a letter to the Head of SEN at the LEA (look it up on the council's website) saying
"I am requesting a statutory assessment of my child, [insert name}, for special educational needs under the terms of the 1996 Education Act."
Then add a para on what his problems are, and what school etc have said to back up what the problems are, and how you feel he will struggle in the future. Make it sound bad, not good at this stage, even though naturally as a mum you want to look on the bright side.
Till you do this , in writing, you will get fobbed off again and again, as the main aim in life of the LEA (and their minions at the school, though your head sounds nice) is to keep your kid on School Early Action plus type schemes (= cheap) rather than to give out a statement and get full 1-to-1 support for a child (=expensive).
Once the LEA receive that letter, and put registered post on it to be extra sure, they are legally locked into an exact assessment process, the timings of which you can find online but I think they have 12 wks to assess.
It is good that the Ed Psych is coming , for an Initial Assessment report - I don't know what this is exactly, but it sounds promising. But ... she is under no obligation to write that in any hurry if you haven't set in motion the legal process. You will get told stuff like "oh, don't start the statementing process too early as he may come on in leaps and bounds and you don't want to underestimate his abilities by starting too early" (a clever one that, as it makes it feel like they are on your side!). It's bollocks, they speak with forked tongue!
I learned this the hard way, as I kept on asking for a statement verbally, from people who I naively thought wanted only the best for my darling boy, and I was fobbed off for 2 years!!! I was so annoyed that I found out that they need do NOTHING till they get a request in writing.
You have to be more cunning than a fox with this stuff! Good luck!