DD used to go to one.
We planned for her to go to a specialist residential school at secondary, as we had been told by independent professionals, that was what she needed long term. We knew she could not cope in mainstream, and there were no schools in the county at secondary, that could meet her needs. We started looking round specialist schools when she was eight. We had her assessed at two of them in Year 5. Both offered her a place. She loved one of them, and wanted to go there. We then started telling the LA, that was what we wanted named in her statement. As it so happened, she was not getting the provisions in her statement and she was being bullied, so a solicitor sent a pre action protocol letter, before judicial review and pointed out they had a duty to keep her safe. At this, the LA amended the statement, to water down the provisions - we took the opportunity to appeal against Parts 2, 3 and 4 of the statement to the SEN tribunal, asking for the school she liked in Part 4. We got reports by an independent speech and language therapist, OT and educational psychologist. The LA agreed to the immediate change of school before we got to the hearing, part way through Year 6.
Most people I know had to start the road to the SEN tribunal, and get independent professional reports, although they might not have had to go all the way to the hearing - but it depends on what your LA is like, and how great DC's needs are?
One head told me half the children at the school had been placed there by their LA, because their parents could not cope with them.