LucyJones, there's lots of good advice here, generally conflicting. I think you do have to see the schools yourself.
I would also suggest finding out if the local education authority have a questions and answers session - ours do one with the NCT - or meeting them, and focussing in on waiting lists, moving schools and catchment areas. If the local school turns out to be bad for the DCs, you can move after a couple of years. Then you would know whether the mega-mortgage was something you had to do or not.
The other thing you could do, depending how bad it all was, would be to rent out your house, and rent in the catchment area of the good school, till your oldest child got in/started. This might well be for about 18 months: in my part of London the relevant address is the place you live when the offer is made, but elsewhere they need you to still live there at the start of term. If they have a siblings policy, you're then safe to move back to your own house.
FWIW, DS1 is just about to start at the least good of the 3 state schools local to us. Not a bad school, just not as good as the others. We have been cheered up by already finding 2 other boys in the same class with parents who are as obsessed with education as we are: if they find some other pals and sit at a table together, the school could work well for us, regardless of its catchment area.