I think it can be done, - I do it, I have to - but to be clear I have a household of 3 adults, not four and obviously don't have any of the expenses of small children, or have to fork out for school stuff.
I save by - cooking everything from scratch - no prepackaged food, and making big meals that last 2 days (i.e. shepherds pie or lasagne etc. I always make a double sized one, then it can be microwaved the next day so don't have to have oven on)
If we want cakes or biscuits I bake and freeze.
I grow some of my own veg. and veg swap with neighbours and friends
I buy basics lines of foods and shop in cheaper stores or on the market for fruit.
I buy my toiletries in Savers or pound shops.
My DH does a lot of shopping around for deals on energy prices, banks prices, insurance etc - lots of good tips on the Martin Lewis website.
I buy clothes in charity shops. I get my books from the library.
But I appreciate it is hard work and not possible for everyone, - obviously I'm not in the depths of poverty - I have a microwave, a garden, a freezer etc - which help me do my money saving things. I also have access to places that it would be hard to get to if you live somewhere with v.bad transport etc.
I also find that when you can't afford things it gets a bit self perpetuating - we can't afford to buy in bulk each month which would be cheaper - because we don't have the cash flow, we have to buy cheap versions of appliances - Sainsbury's basics toaster, microwave, kettle and so on, and they tend not to last as long.