I think people are being really rude and its uncalled for.
With 2 very small children it would be doable but I wouldn't plan to do it long term.
Fresh:
Lettuce 50p, cucumber 50p, salad tomato 80p, apples £1, bananas £1, tangerines £1, carrots 50p, onions 80p, peppers £1, bread 80p, 4L milk £2.50, bag of casserole veg £1, bag of soup mix veg 60p, cold meat/tuna for the children's sandwiches £2, baking potatoes £1
Also seen sweet potatoes for 99p, butternut squash for 50p on offer so cheap soup for the week instead of making a veg one.
Plus a good cupboard supply of herbs, spices, stock cubes, oats and freezer supply of frozen veggies you could do it. For closer to £20 per week I reckon if you add on your meat/ some small treats for the children.
Every now and then you would need to top this up plus butter, cheese etc