Parents can request the local authority consults with schools that are specified in Section 38 (3) of the Children and Families Act 2014. Those are:
- a maintained school;
- a maintained nursery school;
- an Academy;
- an institution within the further education sector in England;
- a non-maintained special school;
- an institution approved by the Secretary of State under section 41 (independent special schools and special post-16 institutions: approval).
If you are asking the LA to consult with one or more, that are within these categories, the local authority must consult with those schools. If the local authority is advising you it can only consult with one school, or it cannot consult with specialist schools, or that school can only be a section 41 school, this is not correct.
It may be their policy but the law is clear and it cannot refuse to consult. That doesn’t mean it will choose to name it. But they must consult with the school you request under Section 39 (2) of the Children and Families Act 2014.