TBF, Op is only budgeting for dinners, and scanty breakfasts, and seems to be happy to serve unhealthily small portions, and apparently lives somewhere where you can buy 500g of cheese for 70p rather than the usual £4.
If I had access to these magical deals, and was only serving one snack size meal a day, plus pancakes made with a single egg between 4, then I could do it on £20 a week too!
But I don't, I think it is important to provide my family with 3 full, nutritionally balanced meals a day, and therefore spend far more.
There is simply no way that a fully healthy balanced diet can be provided for less than £1 per person per day, let alone once you add in the other grocery items such as washing powder, cleaning products, toiletries etc. For me, a decent variety of nutritionally balanced food is the most important thing that I can spend my money on, and I genuinely cannot understand why the OP would think that this level of scrimping is a good thing.
OP if you only have enough money to spend on food, then please contact a foodbank or other agency for help. If you have more funds available, please prioritse a nutritionally balanced diet for your family.