Statistically, you will receive better results at a private school than you will at a state comprehensive school.
This will affect your university application. For example, universities such as Oxbridge may look at your attainment against the average attainment of your school. For instance, if you receive 5 A*s at GCSE but the average at your school is 8 A*s, this won't look as good. Whereas someone from a state school who receives 5 A*s at GCSE where the average for their school is 1, will be looked upon more favourably. It's about your attainment in relation to the rest of your school.