There are two issues.
Firstly, a special school place. If you want a SS place, have you appealed?
For non-wholly independent schools, the only lawful reasons for refusing to name your preferred placement is if the LA can prove:
-The setting is unsuitable for the age, ability, aptitude or special educational needs of the child or young person; or
-The attendance of the child or young person would be incompatible with the provision of efficient education for others; or
-The attendance of the child or young person would be incompatible with the efficient use of resources.
For non-wholly independent schools the LA can, and must, name the school regardless of the school’s objections unless they can prove one of the reasons above. For non-wholly independent schools being full, which is not defined in law, is not enough of a reason on its own to refuse to name your preference. The LA has to prove the school is so full admitting DD is incompatible. The bar for this is higher than LAs and many schools admit. It has to be something tangible and specific and is more than an “adverse effect”, “impact on” or “prejudicial to”.
When you say can’t meet needs, is it that you don’t think they can meet needs or is the LA/school saying this? Because if it is the LA &/or non-wholly independent schools saying it, you can still pursue a place.
You only need an offer of a place for a wholly independent school.
Have you looked out of area but within travelling distance? For secondary, up to 1hr15 is typically considered the maximum recommended travel time.
Secondly, 4 or 6hrs a week is not a suitable full-time education. The LA should be providing more. It doesn’t sound like the education centre has a suitable peer group. Is it a centre where different DC attend at different times? Is the centre planning on admitting more DD’s age/sex soon? There are options beyond the current 4hrs tuition that isn’t meeting DD’s needs and the education centre which also doesn’t sound like it can cater to DD’s needs. Is section I completely blank or is there a type of placement named but no specific placement?