We (2 of us) spend £120 a month on groceries, but we did buy a lot in bulk when we moved (big bag of rice from the wholesale shop, pasta, tinned tomatoes, oats etc.) so if the £120 isn't enough we have the basics without needing to top up, it can be done. We also make food lists, I've got pretty much every meal planned between here and April, so we know exactly what we need and we make sure we use the same ingredients in some meals to use anything that might be leftover.
This way we never have to use anything other than fresh, we get our meat from butchers rather than supermarkets, and our veg, brands etc come from Ocado, you'd be amazed what you can do with a budget, right now my friedge is full of coconut water, almond milk, organic jams, peanut butters and we have bottles of Evian so we don't live on a shoestring by any means.