my advice would be try and calm down
you could maybe look for housing thats on the direct line out, ie
Willesden/Kilburn/Cricklewood/Neasden/Kingsbury/Harlesdon
this is commutable to London, and to N Kensington
you have not let them down, and many many kids in London commute to school, and get the tube to see their mates
I would focus on trying to find a decent rentable thats in a more suburban area but is also not too far from work/schools
I know you are upset, but I genuinely think this is your most viable and realistic solution right now
from a quick glance I can see rents for 2 beds in Harleson for a hell of alot alot less that £1300
Be strong! dont think "horrible areas" as lets face it alot of decent families like you will live there too
if you get SH, well great. But have a plan B and do try and rehtink attitude as if you thing (failed, horrible area) wont get you anyhwere
being blunt, but hope this helps!