Sorry u are in this situation. You, or helpful adult, is going to need to contact admissions offices at schools email or phone. The Good Schools Guide website will have schools by location, with short description.
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Example email or phone type discussion-
Subject: 6th Form admissions for Sept 2024
Dear Admissions Office-
I am writing to ask if there are boarding places available in your 6th Form for September 2024. I am writing on behalf of a young man, your name, that due to circumstances has missed the usual admissions process and deadline.
He is looking to study, (subject 1,2,3,or 4). Currently he studying at XYZ school and is taking GCSE in (list subjects), with expected grades of (list).
I would be grateful if you could reply, or contact me on Phone. If you do have potential open places, we would happily complete the application process.
Kindest regards,
Good luck!!