It depends how much the cat food is but otherwise I think £25 a week for one person is tight but doable.
As another person said it is £3.50 a day. I often try and make our meals for under £1 per head. It won't be particularly lavish but it is definitely able to be done by cutting out a lot of meat, predominantly buying frozen fruit and veg, using pulses etc.
Breakfast - porridge made with half milk/half water and some frozen fruit added. Or the own brand Weetabix is absolutely fine, we buy that a lot. The Tesco ones work out at 10p for two own brand wheat biscuits then with milk added that's breakfast for under 50p.
Lunch - peanut butter sandwich, or cheese and tomato sandwich, or egg on toast, or soup and a piece of fruit. Bananas, apples, pears, plums etc are usually the cheapest.
Dinners - the cheapest dinners I make are jacket potatoes with beans, marmite spaghetti (Nigella recipe) or any pasta with frozen veg and some sauce, pork chops with vegetables, egg fried rice with frozen peas and sweetcorn, daal using dried lentils and spices etc.
E.g. just checked at Tesco:
Bag of own brand penne pasta - 50p
Jar of pesto - £1
Tin of cannellini beans for protein - 50p
Frozen peas - 50p would be half a bag of the own brand frozen peas
Grated cheddar - 50p
That would be £3 but make four meals for dinners or lunches at 75p per portion.
I'm not saying it would be pleasant. I think snacks and treats would be rare but it is possible.