I've seen most of the responses but I'm thinking the OP is actually seeking for our independent indigenous solutions as to cut food cost practically here is my own solution that I've practiced with my family Viz;

Bulk buying from source : I adopted a pattern to buy basic food stuff at the wholesale point of distribution like seafood we choose a good weekend and buy them from direct fishermen when they're back from their fishing we cut, grind and store them doing this helps us to get it cheaper and natural  this can last for more than a month for grains we have contacts in the village that bring them to the city so we pre order beans,rice etc from the farmers.

Home grown food; We also plant basic vegetables in our yard and get to harvest them for some quick fresh food, I remember last Christmas I didn't buy any meat because I made a small cart and reared a few chicken and when it was the festive season I made a small profit buy selling a few and cooked the rest with my family by this I didn't only cut cost but I earned more.

Finding cheaper alternatives ; If the goal is to feed and stay healthy and not just spend money then instead of junk and packaged drinks which may have their disadvantages like excess sugar I buy bulk mixture of fruits and do fruit smoothie this is more healthier for me.... Safer and cheaper