I've been in your situation with my DS at age 15.
He couldn't attdn school school to severe anxiety.
They offerd him a place at a referal unit - tried to sell it to us a 'small safe environment'.
It was anything but!! It was the local Pupil Refrral Unit and the thugs that were taught on teh same site would throw stones at the classroom window and wander into his class to threaten the teachers and pupils.
At that point I said "Enough". I withdrew him stating that the referral unit was not conducive to his medical condition as the violence he experienced there increased his anxiety.
the LA them home educated him by supplying home tutors to come to his house to teach him.
And that's exactly what I would tell your LA.
With social communication problems , possible Aspergers and anxiety your son has Special educational needs.
The LA knows that children with long-term special needs should either be educated in mainstream or special school and not pupil referral units. But they try it on with parents in the hope they can save having to spend money to provide suitable education for your child.
Of course the LA will try to force him back to this referral unit - but you should refuse. he shoudl not be forced to be an in environamnet that's not safe and which increases his already severe anxiety.
Your child should be on a SEN monitoring system called 'Schools Action Plus'. He should probably already have a Statement of Special Educational Needs and if he doesn't then you should apply for an assessment immediately.
Time is running out at13 to get him the help he needs.
And never use the word refusing when saying your son doesn't want to go to schol. That will make the LA think that he's chosen to to go there and it'shis behaviour that's stopping him from going to school.
The truth is that he is an incredibly sensible child who recognises that the school is neither safe nor suitable for him - and that's what you should be telling the LA in very robust terms.
Oncethe LA have to send a home tutor to him they start to realise that it's less expensive to find a suitable school with suitable support than it is to provide 1:1 home tuition. That's your bargaining point.
Best wishes