I live on my own so I plan to use leftovers. Eg if I have a baked potato I cook 2-3, eat one hot and use the others to make gnocchi.
If you have an Asian / Indian supermarket go there for spices, aubergines and mangos.
When you make a family meal divide whatever it is in 4 and freeze one so you have home made ready meals.
I shop at Sainsbury's and Iceland on line and Lidl and the community shop in person.
Iceland deliver for free if you spend £40. Sainsbury's I have a delivery pass, it costs £4 a month for mid week deliveries, it's £7.50 for delivery 7 days a week.
The pass belongs to the person not the address so I can visit my dad and have shopping delivered there.
Don't buy convenience, home made Yorkshire pudding is much nicer than Aunt Bessie's and is cheap.
In your meal plan have a couple of simple meals, cheese and beans on toast, toad in the hole, eggs on toast.
Use all of the vegetables you buy. So if you buy a head of broccoli cook the florets as a veg but use the stem to make a soup or chop to put into a lasagne / shepherds pie. The same with cauliflower.
Use veg peelings for stock. Someone mentioned a slow cooker, they are ideal to make stock, just save your peelings and add water, seasoning and I usually put an onion in. I also put chicken bones in but I think you said you don't eat meat.
If you don't have enough peelings then keep them in the freezer until you do.
I actually have a replica of a WWII booklet issued by the government to help people use their rations. https://shop.nationalarchives.gov.uk/products/replica-booklet-ww2-cookery
It has quite a few tips for making food go further.
I know you asked about shopping but if you can cut food waste then you will save. If you do have food waste that is.