Being raised by a mother who constantly stuck to a budget, I have now inherited that mentality. 90% of the time, in my opinion, store brand will do just fine.
We regularly shop at Tesco (with the odd trip to ASDA or Sainsbury's if life goes that way) and buy Tesco Value in lots of products, I will admit. Some of it is from not having much money (and having lived as a student for the past 5 years!) and honestly not being able to tell the difference between brands! We buy Tesco Value paper towels, tuna, tinned tomatoes, tea, stock cubes, ramen noodles, ketchup, brown sauce, mayonnaise, and various other bits. I will not Value (but will buy store brand) in some things, because it's just disgusting. Very few things, I buy name brand: dish soap, laundry detergent, and things like toothpaste/shampoo, etc.
I personally cannot tell the difference between something like Tesco Value tuna and John West. Tuna is tuna to me. The toilet paper IS cheap, but at the end of the day, we're not trying to impress anyone. I have fairly low standards from growing up in a house of generic/store brands. It's not appropriate everywhere, but I'm pretty sure that brand standards boil down to what you're used to and where your priorities lie. I'd rather buy cheap(er) food and save for a nice pair of jeans or similar!
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We spend ABOUT £30/wk for 2. This varies widely, as some weeks involve stocking up at Iceland's (frozen chicken breasts and bacon, chiefly) or the need to buy expensive things. We try and buy most our fruit at the local fruit stand that operates daily. It's actually cheaper than Tesco (though quality is hit & miss, for all that people go on about the benefits of local produce vendors).