I'm a student, type 1 and lone parent to boot. My weekly shopping budget is £60, however remember that is to feed 3 people, and run the whole household (1-2 washing loads daily, cleaning products etc etc)
So...
My first suggestion is that you menu plan. Work out your main meals so that ingredients compliment each other so you can bulk buy. E.g roast chicken one night, chicken salad next day, chicken curry day 3, and pick bones clean and freeze leftovers for fajitas (in lettuce wraps) another day.
2nd suggestion is to shop around. Collect the coupons from free ads & get a daily bus pass and spend 1 day a month stocking on cupboard and freezer essentials. I did this yesterday and spent £15 in farmfoods ( 10 sirloin steaks, 15 chicken thighs, 10 pork loin steaks, 10 hot & spicy seasoned [not breadcrumbed] chicken breasts, 8 lamb chops), £8 in Iceland (2 bags prawns, 8 Pollack fillets, chicken breast nuggets & fish fingers for kids). £22 in Tesco on cupboard foods (tins, jars, packets, spices, breakfast cereals for kids etc), £5 Chinese market for rice sack (kids aren't low carbing) and spices, £6 on market for washing liquids and cleaning stuff (inc a massive bottle whit vinegar which I use for cleaning).
So far total is £56...but for the month, for 3 people.
Next suggestion is oops shopping for things, Thursday night's most supermarkets reduce a lot more of their fresh fruit and veg and meat (than the rest of the week) in order to prepare for the weekend shoppers... So go then!
Bulk cook if you have things with a short date and freeze, I bulk cook minced beef and onions then freeze in portions. I can use it for Bolognese, chilli, etc. I also bulk cook a basic tomato based sauce. Oops veggies, passata, onions, and oops herbs...blitz in blender and my kids don't know just how many veggies their getting. Freeze in bags and you have a basic sauce for loads of dishes (chilli, Spanish chicken, moussaka, Bolognese- you get the idea).
If you have menu planned you can pick up your veg daily (root veg weekly through oops shopping) and keep well within budget.