For instance, on day one, he adds some mint which cost ~50p to buy, but he calls 1p because he only eats a little. He does not eat the rest of the mint that week, so it cost him ~50p, i.e. half the days budget.
I am poor and eat very cheap. I do that using dry bulk foods and frozen veg. This is important because there are opportunities for free meals (e.g. if customers at work do not eat all the sand witches and biscuits, that can be lunch for 2 days). Friends invite you for dinner too. If you buy food that spoils, opportunities like this come at a price.
How about this for a suggestion - mix lentils, buck wheat, brown rice, dried beans, quinoa. These come in 500g bags for about a pound. You need 6 spoons of this mix per meal, so 10 pounds of mix will last you several months. Put in a rice cooker for 40 min (some beans need soaking first), with a chicken stock cube. Cook for 20 mins then add mixed frozen veg. This will cost you about 30p per meal, and is pretty much complete [1].
I eat the above most of the time, and take free food whenever possible. At the end of the week, I treat myself to a ready meal. You can add curry spice or other herbs for variety. After a year of this I feel pretty healthy.
As an aside, supermarkets are machines for making you overbuy. Between BOGOF offers and big packs of meat (or small ones at a huge premium), it's very hard to shop there on a budget because they are designed to trick you into making 'bad' choices. Avoiding them by living on a non-spoiling diet saves tons.
[1] I think. The key to a healthy diet is variety, but if your basic meal is healthy and cheap, you can make sure to be eating other things from time to time.