Acceptance for primary schools?

i live in the stoke on trent area and my 4 year old son is due to start school in september. Unfortunatley the schools that fall in my catchment area are amongst some of the worst and i do not want him going there. Because of this i have applied to other schools outside of my catchment area but have been told that if he is not accepted i have no right of appeal for primary schooling. Is this correct?