Can I name an independent special school? Does the LA have to consult it?

Yes, you can ask for an independent special school.

The LA must consult with schools specified in Section 38 (3) which includes independent special schools and special post-16 institutions approved by the Secretary of State under section 41.

The LA does not have the same duty to consult with other independent schools, however they must consider the request. Although they are not under the same duty to name the preferred independent placement, the LA must have regard to the general principle that children should be educated in accordance with their parents’ wishes, so long as this is compatible with the provision of efficient instruction and training and does not mean unreasonable public expenditure.