Barbara being a working Londoner doesn't automatically equal having a travelcard, or having one that covers tubes. I travel to work by bus and pay as I go with Oyster so spend £50-60 less per month than I would if I had a travelcard. So trips with DC have to be carefully considered as it's extra travelling cost.
But agree there are great things to do in London for free if travel isn't too much of a barrier. Museums, parks, farms, galleries, lots of free activities over holidays etc.
Op I sympathise, not in the same position but we're in London with DC on just one salary. Food budget is very small and barely any spending money after bills. It's doable and we try to make it fun by challenging ourselves but it can be unrelentingly depressing never to be able to afford clothes, treats, haircuts and so on.
Definitely check out Freecycle. Don't be scared of asking friends and family too - we got a free bed for DS from a friend who was moving.
And yyy to selling things on for a bit of extra cash but beware seller fees if using eBay, best to put money aside until you get your monthly fee statement and know how much they'll take back. No fees on gumtree or FB local pages.