I've just done a sample Tesco order and got enough food to make:
4-6 servings (depending on how much you/your child eats) of tuna pasta bake/chicken pasta bake (pasta, sauce, chicken)
4 servings chicken fajitas (wraps, chicken, seasoning, plus some of the peppers & onions used in the spaghetti bolognese)
4-5 servings spaghetti bolognese with peppers, carrots, onion in for bulk
2 (adult) servings of chicken stirfry with veg, noodles and sauce
Plus 12 bags of those steamfresh veg (as you said convenience) to add to things for some vegetables
2 loaves of bread plus 4 tins of tuna & a packet of honey roast ham, plus lettuce tomato and cucumber for sandwiches and carrots for some carrot sticks on the side
4 jacket potatoes with tuna sweetcorn mayo
Big box of weetabix and 8 pints of milk, plus whatever's left over from the bread for toast for breakfasts
Plus mayonnaise and butter spread as I didn't assume you'd have those
That wasn't me trying very hard and Tesco prices aren't brilliant - but that comes to £57.95. That is me assuming you have oil, salt and pepper - add another say, fiver on if you don't (but you wouldn't need to buy those again during that 3-week period). I'd say if you shopped a bit more carefully than me and did it at a cheaper supermarket, you'll be more than fine!