Let's say I'm Jill Poorbrit. I work 40 hours a week at minimum wage (£7.20) to feed my two children and pay my bills. I should be getting about £1152 with every paycheck, right? That should be more than enough to feed my family for five weeks!
However, then I have to pay £300 monthly on rent, £250 on electricity and running water, and £100 on heat so I don't freeze.
After that is out of the way, then comes about £20 of inedible household products (hygiene, entertainment for children, etc.)
This leaves £482 for meals. Assuming that a meal costs £6.94 as Maxwell calculated, and I am a single mother, so my children would optimally eat £166.56 worth of food weekly. This adds up to the total food cost being £666.24 between paychecks.
Having free lunch at schools would remove £69.40 from the weekly food expense, adding up to £277.60 between paychecks.
With free lunch at schools, I would have £93.36 remaining to spend on food for myself. Without it, I would be going into debt by nearly £150 and would need to cut back on my children's meals at home.
By the way, the meal cost in the OP is wrong on more than one level. Not only is your addition off, you aren't calculating price by individual serving. You're calculating it by the price for purchasing an item, artificially inflating your meal cost. I'd doubt an average school lunch to go above £5 before a la cart items.
EDIT: I'd completely forgotten about taxes, but it's too late to factor those in at this point.
