At my catholic elementary school in 1951 a small number of girls were taken into the head nun's study for extra coaching each year. They were mainly the daughters of parents who were deeply involved in the life of the church. Some of them were clearly not able to benefit from the grammar school curriculum and left after a term or two. Grammar schools were the bastard children of public schools and often copied them, such as setting homework, (which was originally intended to keep boarders occupied in the evening), uniform, and the house system
There were many very poor grammar schools, even though they received a disproportionate amount of the resources available for education. Even the 'best' schools were socially divisive, often splitting siblings on the basis of one test. Stupid parents would 'reward' successful entrants with a bicycle or similar present - what message did that give to the ones who didn't pass?
I will take a guess that all the parents clamouring for more grammar schools have children that are likely to pass the exam, albeit with some pressurised coaching.
Most European countries manage to educate all their children in comprehensive schools but of course Britain is still bedevilled by privilege and lack of social mobility.
As long as the likes of Blair, Clegg and Abbott use their wealth to buy privilege things are unlikely to change.