I would reiterate what Bluebrick has said in that really all your mainstream school can say is that they have confidence your child is a good candidate for a special school. I'm glad you have found them trustworthy.
The local authority is not yet in a position to even consult with schools until they have agreed to issue, which will hopefully happen soon for you. At this stage in the year, unless you live in an area with a load of provision, (where is that magical place?,) the special schools will be starting to finalise their cohorts from around mid January and places will be pretty concrete from mid Feb. There will be space for a few negotiations between school and LA ("we will take x child based on band 5 funding etc) and room for a couple of tribunals, as space itself isn't a reason, though in practice...ugh I better not even go into it but it tends to shut things down for all but the most unusual of circumstances like a looked after child or services relocation etc).
I hope you get your place but if you expect the LA will:
- Blindsight you by suddenly refusing to issue or
- Blindsight you by suddenly naming a mainstream you have never heard of or don't like, forcing you to tribunal, whilst your child is meanwhile out of education (which is why you need to read up on Section 19 provision if you work, or prepare for your child to "fail" at mainstream which is what they want them to do in order to justify a place at special).
...if you expect either or both of those things to happen, you can be prepared, and it's a bonus if it doesn't.
I've seen it so much. I've been working in this area for years and I must take 15-20 phone calls a week from parents who want their child to attend our school who have been gaslit and they have no idea of their rights.
Go on the Facebook group,SEND reform UK or Birkett Long solicitors EHCP and send law advice group and you will see what I mean.
I don't want to ruin your Sunday, but I do want to manage your expectations because you might need a bit of fight and knowledge is power.
I hope you are one of the lucky ones but the timing of all this is not on your side.
Genuinely, best of luck 🙏