All those people should have been involved during Year 9 when a Transition Plan to determine your child's post-16 is supposed to be agreed by all the Agencies involved.
It seems from the amount of posts on here about post-16 education that the Year 9 Transition Plan is not being drawn up. It's the Head's responsibility to ensure that one is compiled. Also, with a Statement, Connexions used to retain responsibility for the young person right up to age 25. I don't know if that responsibility transferred to LAs when Connexions was disbanded.
Statements end when a child leaves school. If the child stays in school post-16 the Statement remains in force.
However, if the child leavs school to attend a FE College the Statement ceases. You can appeal against cessation of the Statement.
It's a (was and probably still is) a very grey area with LAs saying they have no responsibility for the child post-16 when they have completed their statutory education. The school leaving age is to be increased very soon, and I have no idea how that will affect things.
However you also have specialist school that will accommodate sudents up to age 19. You also have sixth forms within schools that are not actually classed as schools but are actually FE provision. So you need to look carefully at the exact status of provision.
There was no way my DS could have got himself to FE College every day and stay there while he was so anxious. Specialist FE College for ASD was the only way to go. You need to speak to your local college to see what they can offer, starting from the momemnt your DS leaves the house - after all, if he can't get there then educating him there is impossible. As a 16 year old you should not be expected to ferry him backwards and forwards - at 16 he's an adult in the eyes of DLA etc.
That's why I suggested contacting the indie FE College of your choice and discussing fuding etc with the, You may well discover that places for next Sept are already provisionally booked - they fill up very quickly.
Post-16 is an issue that is going to feature prominently on this board as children reach 16.