There are both private and state schools just as the Philippines. I suggest you telephone your local education authority to find out which school near you has vacancies - but bear in mind that due to a completely different curriculum, your son may find himself in classes with students one, two or more years younger than him.
I had no problems enrolling my two Filipino stepchildren (then aged 7 and 9 years) with our local junior school in North Yorkshire... via the local education authority. They were on dependent settlement visas.