Well after a night of 'sleep' I have a much clearer idea of the situation and myself.
1- The child does not have SEN. Of that I am sure. The private schools they applied for do not have SEN provisions. The child is now going to a state school because they can't quite afford the private fees. I won't go into more details on this as I want to keep anonymity for myself and them.
2- I have now understood why this disturbs me so much. At this point, if fraud has been committed, an unknown child has been kicked out of the way to make space for hers. I am disturbed by the idea that she would most likely do that to MY child if s/he got into the way of her child. I have never met a parent who (might have) has done this. If this has happened, it makes me very uncomfortable to chat to a person who thinks her child deserves better based on the fact that s/he is her child.
3- she is not my friend. I have a good knowledge of what goes on into her life despite not being 'friends'. If she were a friend I would sit down with her, talk to her openly about this, and if this was indeed what she did I would make sure she knows it's unacceptable behaviour and there could potentially be very serious consequences.
4- I wondered whether I should report because some years ago a case 'exploded' about a school near to where I live. It became clear that a large number of parents had fiddled with the documents in order to get their children into said school. This became quite a news locally. What's the difference between lots of parents doing this or one?
5- I do have many acquaintances or more or less close friends but I would not want to discuss this with them. Why would I? Much better to talk about it with people I/she do not know given that no one is hurt at the end of the discussion.
6- I won't report her, too much emotional investment. I would not care to know the final decision if I reported, that was not my point anyway, nor would I want for her child to be kicked out of a school, he has no fault. But if rules are rules (and we are not talking about music in 1930s Germany) then breaking them at someone else's expense is not right. This is an extremely affluent area, maybe if she did commit fraud she took away the place of a very rich child who can afford top fees anyway, but maybe that child is not well off at all, and maybe that child should have had a top state education because s/he rightfully lived near the school (though as I said earlier it might be that the system is so broken that this last point does not make much sense in the big scheme of things.)
In any case, given that I do think she has committed fraud, adn despite not being able to stop seeing her, I will detach myself from this 'relationship' as much as possible, because I do not feel comfortable with it.