It's going to be a tough call to do it long term, but these threads (you can search for others) are definitely the right place for advice, recipes, shopping plans, etc. Especially if you can let people know your dc's ages, preferences, any allergies, etc.
A drop in income often goes hand in hand with one or more adults having more time for cooking/shopping. If that applies to you, then that's a bit of help to start with.
Presumably as you already know your figure of £40-£50, that means you've already worked out a budget, which included claiming all benefits, free school meals, etc., that you might now be entitled to? Another thing worth doing is checking your direct debits, just in case there's something going out that's no longer relevant/needed. I found and cancelled a subscription to a magazine that my dds had grown out of, which I'd forgotten because my dh had just been chucking it away when he picked up the post 
. Only £5 a month diverted to the food budget, but that's £1 a week, and £1 is a bag of spuds.
If you have a freezer, you could find out when the best time of day is for reduced offers, and buy meat, etc. at those times. We had to lose the idea of meat being a staple. Basic ranges can also be good - among the chemical crap there are many items of decent quality. Generally, the fewer ingredients something has, the better the quality of its basic version. I think there are even a few threads on here recommending the best things to buy from basic ranges.
Setting up with chickens and the like means you'd have an initial outlay. But would you have any neighbours who'd swap a bit of mucking-out for eggs?