Hello CrazyCatLady!
I hardly ever go to Tesco but I'm a regular at Asda. The first thing that comes to mind is their meat-free sausage mix. It looks like gravy granules, you add water and leave it for a few minutes then shape it into sausages and grill/fry it. There are two types, Lincolnshire and black pepper, and both are very good. I cook that with beans and potatoes for a quick lazy meal. You can find it in the aisle with instant noodles in my store (Watford).
They also do their own soy yoghurts which are a lot cheaper than Alpro. However they do have a much stronger soy taste which I personally don't enjoy, so I spend the little extra.
I shop for two vegan adults, my weekly shop would be something like this:
Fruit
Citrus: Oranges or clementines or mandarins
Stone: Nectarines or peaches or plums or apricots
Bananas (10 of them, we love bananas)
Whatever exotic fruit is seasonal/on offer. This week I bought figs.
Veg
Aubergine/laucki (also called doudi or bottle gourd)
Potatoes (about once every 6 weeks, large bags)
Cauliflower/broccoli
Spinach/greens/kale
Butternut squash
Chilled
Pure spread (every 6 weeks)
Soy yoghurts
Frozen
I keep a permanent stock of sweetcorn, peas, mixed carrots/swede, bindi (okra) and cauliflower florets in the freezer, replacing when needed.
Asda's own Meat Free Mince
Occasional Linda McCartney products
Bakery
Bread as needed - we just get a half-loaf
Part-baked baguettes
Cupboard
Sausage mix
Fat free supernoodles (tend to be vegan, but not all flavours)
A tin or two of soup
Baked beans
Chopped tomatoes
Bulk bag of pasta when needed
Crisps
Chocolate/sweets (Fry's mint cream bars are vegan, and Asda do several varieties of vegan sweets like the strawberry laces)
Lemonade or other fizzy drinks
Every few weeks I go to the health shop after to get some speciality vegan 'meats' or pizza or something to put in the freezer for a lazy day.
I advise you to rotate your fruit and veg. Try to get different colours in each shop, it's generally a good way to make sure you're getting a range of vitamins and minerals. Buy what's in season since it will be cheaper and of better quality. Find a balance between sticking to your favourite 'cupboard' items, or looking around and spending hours reading labels. I tend to buy the same stuff but I always make a point of going to the Meat-Free freezer section to see if there's anything new, and occasionally browsing an aisle to see if there's something accidentally vegan I haven't noticed before.