Sorry for your disappointment, it can be really gutting at the time for both child and parents.
A couple of positives. Whether you qualify outright or on appeal, it makes NO difference to your chances of getting a place at any particular grammar, however popular. Those who get through on appeal will go into the same pot. The ONLY criteria are distance, siblings, catchment, etc. So, in theory, all other factors being equal, someone with 118 who got through on appeal but lives nearer would get preference over with 141 who lives further away.
It would help to have something from his prep school. Did they do Ket stage 1 SATs? Do they do any optional SATs of CAT tests? Even if the school do not support the 11 Plus, they surely can't object to confirming that your son is academically well above average? There are plenty of state primaries who are also uncooperative, but usually something can be squeezed out of them. Without any academic evidence it will be difficult, but you don't need the school to say that they believe in grammar schools or to accompany you to the appeal.
Hope that provides some encouragement. I'm sure others will help too, and look at the appeals section.