I lived outside London and I was 1.5 miles from the nearest station (there was only one nearby). But that station took me directly into a major terminal and from there it was only a short walk to my office. And, more importantly, I wasn't at risk of being priced out of where I was living, because I wasn't privately renting, and in any case, I didn't have children so the consequences of being forced to move wouldn't have been anywhere near as severe as they are for the OP.
London is vast, and if you have to change trains or tubes several times to get to work, it can easily take as long to get to work as it took me to get in from 40 miles away.
I don't think it's very helpful to post Rightmove links to flats in random parts of London when you don't know the OP's circumstances.
We know she is concerned about having to uproot her son and move him to a different school. Realistically, unless she stays pretty close to where she is now, he can't stay in the same school. So if she moves to a random part of London where the rent is cheaper, it is going to disrupt his education, his friendships and potentially his childcare arrangements.
And nobody is acknowledging the issue that even if the OP does as you are suggesting and moves to a random flat in North London because the rent is cheaper, (with all the associated cost and hassle of moving such as agency fees, finding another deposit before you've got your old one back, fighting to get your old one back because letting agents are invariably arseholes, removal costs, time off work etc etc etc), in a year or two she could find herself priced out of that area and in exactly the same situation again.
Where does it stop?