Starmer's school was only a state grammar for around three of the years he attended. He started 1974 and the school then became private fee paying in 1976 (equivalent of approx £20,000 p.a. today.)
Starmer attended the private fee paying school from 1976-1981.
He was a junior exhibitioner at the Guildhall School of Music and Drama until the age of 18, and played the flute, piano, recorder and violin. Not your average state boy at all.
It is strange that even though easily readable on Wikipedia etc, there is still the myth that he's a state educated boy.