"Hakluyt. Local schools are comprehensives, as shown in the livery on the schools' billboards. "
The non-grammars in a town with 4 grammars in it are CALLED comprehensives - but they are not. What a school is called on the billboard - comprehensive, high school, academy, secondary school, upper school - is not the point. Because a school can call itself, within reason, what it likes, you have to look beyond the billboard and actually consider the intake.
Comprehensive = representative intake from its local area.
Grammar school = intake not represemntative of local area, selected on basis of passing exam, usually at 11. May take anything from top 25% - top 0.1% of ability
'Secondary modern' / 'Other school in a grammar area' = intake not representative of local area, default for those not passing an exam for a grammar school.
I would say the dividing line between comprehensive and secondary modern / 'other school' is quite a tricky one, but perhaps where 2% or more of the higheser ability children from the local area are removed to a grammar school? Those, say, 6 children per year DO make a difference.... difference between 0 and 6 Oxbridge entrants, for example, is HUGE in terms of public percetion and pupil aspiration.