DD is in Key Stage 1 (so 30 limit on class sizes).
I've rung round all the schools in the area and they are all full. The LEA have said that they would place her within a 2 mile radius if all schools were full. I don't know how they would do this. I'm presuming that they can force a school to take a child despite class size limits, under certain circumstances.
I've rung round all the schools in the LEA 2 mile radius too and there is only one school with a place that might be coming up.
However, our last experience of this one school was driving past it with children running out of the playground with rocks (from a skip) which they were throwing at each other. We had to swerve to avoid them. When I got out I had a volley of abuse from them!
There is no way I would send DD there. However, could the LEA say that we had to take the place? Could they refuse to place her in another already full school if there is a place at this school?
As far as I understand it, they only have to offer you one place - if you don't want to take it then I don't think they have any further responsibility to find you another one. If the other schools are full and this one has a place, then I think it's unlikely that they would force another school to take a child just because you "don't like it". (I know your feelings are based on more than that, but the LEA will take the view that all their schools are just fine thank you very much)
You would then have to look for a place further out yourselves, go private, or home educate until a suitable place becomes available.