THIS POST IS NOW TO SOME EXTENT OVERTAKEN BY THE DECISION OF THE UPPER TRIBUNAL HERE
The short answer is maybe.
What happens in a maintained school?
If a statement of SEN names a particular maintained school, then section 324(5)(b) requires the governors to admit the child. That gives the pupil an absolute legal right they can enforce by judicial review.
What happens in an academy/free school?
The position with an academy/free school is more complex.
As with most things about academies/free schools, the starting point is the funding agreement for the particular academy/free school. But beware, funding agreements vary. So always check the agreement for the particular academy/free school you are considering.
The newest academies/free schools set up using the latest model funding agreements are likely to have the following in Annex C of their funding agreement (but older ones will vary):
“The Governing Body of the Academy Trust must comply with all of the duties imposed upon the governing bodies of maintained schools in: Part 4 of the Education Act 1996 as amended from time to time …”;
A footnote in the funding agreement may well then explain that:
“Currently these duties are in sections 313 (Duty to have regard to the Special Educational Needs Code of Practice 2001); 317 (Duties in relation to pupils with special educational needs), 317A (Duty to advise parents that special educational provision is being made); and 324(5)(b) (Duty to admit the child where a school is named in the statement).”
In other words, an academy or free school with a funding agreement in those terms is required by its funding agreement to admit the child whether or not it wants to. From the point of view of parents/pupils, that puts them in nearly the same position as they would be in a maintained school. I say nearly because there is still an issue about whether they can force an academy/free school to comply with its own funding agreement.
But by no means all funding agreements are in those terms. Some say nothing about the circumstances in which the academy must admit the child; others say only that the academy shall admit the child where it has consented to being named; others also refer to admitting a child to comply with an order by the SENDIST; but lots say nothing about the situation where a local authority has just gone on and named the academy anyway (the implication perhaps being that the academy can resist admitting the child in that case).
However, there may nonetheless be a futher argument, even in those cases, arising from the fact that all academies/free schools now take effect under the Academies Act 2010 which includes a requirement that “Academy arrangements in relation to a school within subsection (5)(a)(i) must include provision imposing obligations on the proprietor of the school that are equivalent to the SEN obligations.” where “the SEN obligations” means “the obligations imposed on governing bodies of maintained schools by … Chapter 1 of Part 4 of EA 1996 (children with special educational needs), and … regulations made under any provision of that Chapter.” That could mean that even where the academy funding agrement does not include an obligation to admit the child (in the circumstances in question), such an obligation must be ‘read in’ to the agreement. As far as I know, that argument has not yet been considered by a court or Tribunal.