The thing is, if the OP is, at this stage, still a long way down the waiting list it means that she is, almost certainly, too far from the "good" schools to have been offered a place in the initial round.
Sorry, OP, but that's the harsh truth.
So, while there is an issue about lack of school places in some London boroughs, this isn't the case here.
In this case, it's more that there weren't enough places in the "more popular" schools to go round.
OP - go visit the "poor" schools. I can guarantee that there will be dc like your own and parents much like yourself at those schools. And yes, quite a few of them will be on the same waiting lists your dc are on.
I can see why your incredulity is coming across as sounding like a sense of self-entitlement. There is something amazing about the disparity between what is available in schools in the state school system.
I have enormous respect for people who send their dc to the local school, irrespective of whatever, and I do understand how some of the disparity arises, and I realise that some of the criteria on which people judge a school to be "poor" or "good" is (imo) extremely questionable.
But that said, it sometimes is quite a shocking experience to go visit a variety of schools and just be amazed at what is provided in some and not in others and to realise, with shock, that access to excellence is not uniform and not a given in a state comprehensive system that most people, by default, have to send their dc into.