I am so sorry to hear that your son didn't quite make the 121 mark.
However, both his marks are within the recognised "appeal zone" of 116- 120, and one of them is very close, so I think you should go for an Appeal.
Your first preference is Burnham Grammar, and the basic
Bucks appeal documents need to be submitted within 14 days of the result, i.e. 7th December. That is the same day as the Berks results - who designed this system?
So you should apply for a Bucks appeal hearing in the meantime.
You may be able to avoid doing too much paperwork for the Bucks appeal ahead of the Berks results, and that will take some of the stress out of the situation for you.
This is going to be a trying couple of weeks Sue, but we will all guide you through it and help you in any way that we can.
In the meantime, enjoy that glass of wine, and either post back on "Appeals" or PM me.
My best wishes to you and your son.