I spend around that, but I don't have a man in the house. They do eat more!
However, it is possible. Do you live near a market? If you do, then you can easily buy masses of fresh fruit and veg really cheaply.
Also, my big tip is to simply avoid supermarkets if you can, or to only take cash with you, and only enough for what's on your shopping list to avoid impulse buys. I go once a week for the big weekly shop where I buy meat, fish and milk for the freezer and manage to limit expenditure to about £25-£30. The other tenner is for the market.
Get into offal. Liver, kidneys, hearts are very very cheap and incredibly full of nutrition. And if your kids get used to it young enough, they'll like it. I try and serve offal at least once a fortnight, and fish twice a week.
Plan your menus. This will focus your shopping and minimise wastage.
And avoid processed foods and ready meals. They cost more.
HTH!