Being a single parent is a hell of a lot more difficult than being in a partnership; there is literally no-one else to cook when you're sick, or anyone to care for the child when they're sick, or any number of supports that so many people take for granted.
It's v easy for people in partnerships to talk loftily of saving money by never eating out but if the OP never went out she'd never get to chat with another adult. I don't think £20 a week on an occasion that brings companionship and a break from drudgery is a waste, I'd see that as self care. Enjoy it.
The opportunities for reducing spending are probably in places like finding new providers for insurance, WiFi, phone etc
How long will it take you to pay off the loan?
I recommend opening separate accounts for each expense e.g. power, insurances, WiFi & phone, car (include all costs across the year), loan, Christmas & birthdays, and open a savings one too. My bank let's me do this at no cost.
On payday, I pay into each account accordingly. I also have the direct debits coming from the individual accounts so they sorta tick away on their own. For example, with my car costs, I only need to pay service every 6 months but the money is always there, it's never an unexpected cost. Even haircuts, shoes etc need to be accounted for. Stick £50 into the savings account and forget about it.
With regards to food shopping, could you try shopping online instead? In that way, it's easier to stick to your list. Perhaps settle on 3 regular meals that you'll eat each week and always keep the ingredients on hand. On the weekend, make twice as much as you'd eat and freeze half for a week night.
Try making one change a week, perhaps, so you don't feel overwhelmed. In about 3 months, you should notice that things are more manageable.