Minutes seen by The Times of a recent meeting held at St Olave's Grammar in Orpington reveal that Aydin Onac believes allowing certain students to continue their studies would not be in their best interests.
A number of parents threatened the school with legal action over the summer after their children were prevented from beginning their second year of A-levels because they didn't achieve at least three B-grades in their first year tests.
The move was criticised by government ministers who warned that excluding a pupil for any reason other than bad behaviour was against the law.
Approximately 15 students were allowed to re-join St Olave's to continue their studies this term after some mums and dads threatened a judicial review.
However, the newly-released minutes reveal Mr Onac still expects pupils to attain at least three B-grades in order to continue their second year of A-levels.
At the time, St Olave said it operates a policy to maintain what it calls its "exceptional A-Level results". Dating back to 1571, it has sent a significant number of pupils to the country's top universities.