It's very doable. I don't budget that carefully and would mange fine on that. A few ideas:
Shop in Lidl and Aldi. You'll be amazed at how much cheaper they are. Eg an Aldi malted bloomer loaf and a 4 pack of their beans would cost about £4. Both delicious (search old threads, Aldi are way better than Heinz beans) and for under a fiver you have lunches or breakfasts for both of you from Monday to Friday of beans and toast. Box of eggs and another loaf and you've got French toast or scrambled eggs to mix it up a bit.
Here is a recipe for chilli as an example of a healthy, filling recipe that you could get ingredients for, for well under a tenner, including a pack of rice or couple of sachets of cooked rice from the above discount supermarkets. Cheap higher fat beef mince will be fine, maybe even tastier. That's dinner for 2 nights taken care of. I like it with the 80p tortilla chips from Lidl and maybe some grated cheese to mix things up as a treat weekend dinner.
Porridge oats £1ish a bag for the cheap ones (no different imo). Make with water or milk in the microwave for breakfast or a snack.
Lentil soup - couple of leeks and carrots (£1.40 and 70p a pack iirc from Lidl), couple of stock cubes, mug of lentils (not more than £1.50 a bag) boiled up. Fling in a potato and onion if you have them. Mash with a potato masher to break down. Delicious dinner with bread or maybe a cheese toasties. You'll get 4 portions for well under a pound a serving.
Use some of the lentils left from your soup to make daal. Add a couple of supermarket naans to dip.
Get the Lidl phone app. This month you get a free bakery item every time you shop. I got a couple of donuts and a baguette so far. The baguette goes well with lentil soup.