GrandmaMoira,
Academies don't set entrance exams, although a few are allowed to reserve a number of places for children who are gifted in (for example) music. They use it as a backdoor selection policy, which actually means that children of pushy parents are more likely to get into 'good' schools.
A few schools use assessments such as you describe to try and achieve a balanced intake, but this practice has almost died out since schools have become responsible for their own admissions policies. It was an attempt to avoid people moving into catchment areas just to get their children into the so-called 'best' schools. It didn't mean that brighter children had less chance of getting into a good school. It meant that all schools had the chance to be good schools.
Where did you hear this, GrandmaMoira? If your grandchildren live in or around London, they're taking tests, because so many of the schools are voluntary-aided and semi-selective. Children don't have to take the test, but the sharp-elbowed middle classes choose to make their children do them, often paying tutors a fortune to spoonfeed them and causing themselves a deal of worry. The population density also means that it's relatively easy to go to a school in a neighbouring authority, where a handful of grammar schools still exist. People also play the faith game.