By the way, we live in a grammar area but it's one of those small grammar areas surrounded by truly comprehensive areas (outs self). It has made our secondary provision a huge mess:
One of the grammars has boarding provision and this is taken by non-resident families (OK some are military which, fair enough, or families that have moved away, but some are families that do indeed live in Hong Kong). However it is also possible to get a lower mark on the exam and go boarding.
The grammars have a catchment area meaning that those even 4 or 5 miles down the road (so, same education district) have to achieve higher marks. This doesn't make the grammars local schools, though, children come in by bus, train and I'm sure Mummy and Daddy's taxi service (at least I don't see those as we don't live that near the grammars).
Families of course hothouse their children, I'm a Guide leader so see a lot of this, the one family I know who "just tried" with a very bright 10 year old missed the mark by a whisker.
There is one church school with a really good (and fairly academic) reputation but that is also very difficult to get into.
So the other children are left with secondary moderns by default, even though the grammar schools take a very small proportion of the population. This is partly a local oddity but it's also a result of the grammar schools. We could have "very popular church school" and "decent comps" but we can't have "very popular church school, grammar and comps".
Even if primary schools were able to tutor only the children who weren't getting extra tutoring (who? FSM children? Those whose parents weren't tutoring them, or who at least whose parents told them not to let on they were being tutored?), then the differences have set in by the time children start nursery.
Some families have less access to educational materials, some parents talk less to their children) and they continue while they are in nursery and primary school (so even if you say no tutoring, or we'll tutor all children the same, just the extra help from being in a home where parents use high level language, informally teach them maths as they go along, and talk about world events and logic.