I don't think you should have rose-tinted spectacles about social skills provision within special schools. A programme may be designed by specialists, but delivered by members of staff who don't have high-level training: it may include small group card games, and the like, which would be delivered in a very similar way within mainstream
Depends and why is why a super tight EHCP is worth it's gold. More of the independent specialist schools have onsite speech and language and occupational therapists. They usually run the intervention programmes and social skills groups. If you also have an EHCP that states "X needs social skills to develop on X skills, for 45 minutes a week, with no more than 5 peers in a group, delivered by a SLT". You u would get this.
An EHCP can also state what type of training the staff/specialists need to have to run these groups. Please do not put down social skills as something like playing table top games. They would work on conversational skills (which has so many levels) social communication, regulation etc etc.
I agree about the poster who says that independent specialist schools are very selective in their criteria of children that they take and they are expensive.
FYI- mainstream secondary is about pushing exam results and Ofsted. Therefore, SEN children usually get left behind. I've heard of many bright children with ASD and learning disabilities in Adult care services or mental health facilities who have broken down due to the fact that their needs were not supported in the earlier years. Please do not be swayed by the things mainstream or specialist schools have to offer. If you are armament to have your child in mainstream, apply for an EHCP, commission independent specialists and get a water tight EHCP.
If you like a specialist provision, but are worried about academic and grades. Opt for an extended day provision where the LA can pay for 1:1 tuition and place your child, part time, in GCSE facilities of some kind.