I will chip in here with a few comments. They are not comprehensive but they are some early thoughts.
“The evidence in the folder fully supports that his maths is at a level that would endorse him being suitable for Grammar
That comment should be extremely helpful at an appeal, given that the only weakness in the 11+ was his maths score. Both the other scores were very strong indeed.
Despite very high scores in his verbal 11+ tests the folder does not support his verbal/literacy work as being seen as suitable for Grammar”.
The test has proved otherwise - the work in the folder may not have been of the expected standard, but he has proved his ability and potential with the VR and NVR scores.
We were then told that when we appeal, we will have to appeal on both maths & verbal (despite the 138/140 & 132/140 scores!).
Your appeal is against non-qualification on all fronts, but the real task is to prove his mathematical ability, through any evidence you have. If the letter does indeed state what you have quoted, that is another very useful point to add to your case.
I’m really struggling in not just visiting a solicitor to take this up legally as clearly our son is being discriminated against.
A solicitor is not necessary for a school appeal - indeed, appeal panels will often scrutinise cases with legal representation far more closely than those presented by parents alone. I don't think that you can go as far as to say that your son is being discriminated against - merely that the system tends to be "one size fits all", and your son is "a slightly different fitting". That is inevitable for the small minority of Home Educated children.
Anyway, rant over!
I understand the rant completely, having been through an appeal (failed) myself many years ago, but I do feel that if you can focus your efforts on simply preparing a strong case for your son and leave the anger behind, it will be more productive. You have time on your side, so calm down and make the most of that advantage! I had less than two weeks to understand the system and prepare my case (or so I believed at the time - I could have bought more time if I had been better informed), and that was in the days when there was almost no information on the internet and this website was a babe-in-arms.
Really want I want to know is if there is such an item as a policy or procedure for how the 11+ is run? What the rules are etc? Kent admissions seemed to clam up when we requested it and became very vague about its existence.
There will be an agreed Admissions Policy for the county, and that has legal force under the School Admissions Code, but I don't think that is where you should be looking in this instance. It is extremely unlikely that your situation would be proved "illegal".
Also, I know the advice has been not to mention the procedure/system, but bearing in mind that we should have written evidence to support the above injustice, would the advice be the same?
Yes, every time. Please listen to those of us who are telling you that kicking the system is not the way forward. You need to prove your son's ability if you are going to convince an appeal panel. His VR and NVR scores are very good and if the letter contains the statement you have mentioned, you have moved forward another step.
I am glad that you have posted on here because I can recall very few cases for appeals for Home Educated children. I will certainly be on a learning curve, as will others on the forum. Hopefully it is one that will benefit your son first and foremost, but also others in future.