But when the state says that a special school of choice (or state school of choice) does not have space for your child and admitting them is prejudicial to the effective education of others, is that not also ‘state interference in choice’?
The government is not required to provide the education of your choice. The ECHR devotes quite a few paragraphs to making that clear.
If the state raises NI and so private schools have to raise fees, is that ‘state interference in choice’?
It's for the courts to decide.
But I'd suggest that an NI change affecting all businesses is quite different to a new tax which is so targetted that e.g boarding provided by state schools is not taxed, but the exact same boarding service provided by private schools is. Same for paid extracurriculars.
Especially when Labour recently tried to ban the sector which they are now targeting so precisely. Personally I think that makes their intent quite clear.
If a state body responsible for safeguarding or child welfare visits a setting and declares it unfit, is that ‘state interference in choice’?
The ECHR rights are very clear about this. There are multiple rights to balance. The child's right to an adequate education overrides the parent's right to choose their education. So if the parent's choice of education isn't adequate, then the state is permitted to refuse it. However so long as the parent's education is adequate, the parents take precedence over the state. Again, there are quite a few paragraphs making that clear.
What does, and does not, constitute ‘reasonable interference’?
That's for the courts to decide.