Ok, lets unpick this.
It is not illegal for the LA to share your application form with schools. It is poor practise, but it is not a breach of either the Admissions Code or data protection. Indeed, the application form is often included in the bundle of papers sent to the appeal panel, so it is possible it was shared with the school for this purpose after decision letters went out.
The critical point in what was noted by the SENCO (which may, of course, not be an entirely accurate account of the conversation) would appear to be that you were late, if that is correct. If you applied after the deadline your application would only be considered after all the on-time applicants. Unless the school was under-subscribed, you would not get a place. It is also possible the admissions officer commented that you named the school as third choice and the SENCO, not understanding the admissions process (many don't), wrongly assumed that was part of the reason you didn't get a place.
It is extremely unlikely that the LA is colluding with the school to allow them to operate a "first preference first" policy. It would be very obvious to the LA if this was happening when the school's ranked list of applicants came back.
It is not uncommon for head teachers to state publicly that applicants won't get a place unless they name the school as first choice. Many don't understand the admissions process. Some deliberately mislead parents in order to get more naming their school as first choice.
It isn't entirely clear how or why you informed the LA that you were thinking of moving south. If this was on your application form, the school would have found out when it was shared with them.
The fact you decided not to move when you didn't get offered a place at any of your preferred schools suggests that the schools were in the area to which you intended to move (which is also a likely reason for you missing out on places). If that is the case, it is not unreasonable for the school to infer that the fact you applied meant you intended to move. That would not involve the LA sharing this information with the school at all.
If the academy is actually operating a first preference first policy they are clearly in breach of the Admissions Code. However, I'm afraid the information you have disclosed falls a long way short of proving that.
If you want to pursue this, you will need to refer it to the ESFA. They can get the clerk's notes from the appeal. The clerk was quite right not to share them with you, by the way. That would have been a breach of GDPR as it would have told you what individual panel members said about your case.