Both my children were good readers before they started school and a good primary school should have no problem dealing with this, certainly the primary school my children attended were unfazed by it.
DGD, starting school a year earlier than her parent's generation, was just starting to read when she went to school and was given her head when she got there and 18 months later she is now an excellent reader.
The school she attends has a very mixed entry, children from a council estate with high levels of deprivation and others from an estate of medium sized 1930s semis occupied by graduates and other professional people, so the reception class faces everything from children who have never been read to and are unfamiliar with reading to others, like DGD who are already starting to read. There is no sign that this causes the school problems.