Huge sympathies that catchments are so tight and competition for favoured schools so high. V disappointing for you.
Don't give up on waiting lists, there is generally loads of movement before school starts, and places come up even within the first 2 weeks of term.
However, you don't really do yourselves many favurs in your advocacy.
Why didn't you put down your NEAREST school, or your 2 nearest schools, after your 2 preferred schools?
My DP had EAL when he started school and has a top English degree now. It is a myth that a school with EAL speakers in Reception 'holds children back' Apart from anything else, children who have more than one langiage have a better cognitive understanding of what langage is and how it function s because they make a connection that a word is a symbol for an object much quicker.
Also, schools which offer good support for children with SEN are often the best schools for everyone. Children with statements will have their own 1-2-1 support from a separate additional budget to the school, and are often in a group or unit which gives them the specialist attention they need just as gifted and talented children will be in yet another group when appropriate for 'enrichment' or whatever.
And why the Local Authority has any obligation to ensure that you don't have to go into any particular area on your way to school, I don't know.
There seems to be an issue in Hackney, of not enough places, not enough favoured schools, or good schools - but you need to advocate for more better schools with a spread which matches population density or whatever, and not make judgements which reduce your case to one of not wanting to ix with certain children or go into certain areas!