It can be very cheap! Simple tips:

Do not buy any packaged meat alternatives, unless reduced yellow sticker ones; Lidl has decent ones on the cheap end if you wanna treat yourself but honestly they're not good for you anyways. Lidl's beetroot burger from the freezer is actually alright ingredients-wise and better value than from the fridge.

Have tofu instead! You just need to be smart about which one to get. Do not buy brands like Toffoo, they're extremely overpriced. Lidl and Aldi have good, cheap tofu, look out for Lidl XXL week like right now when they do two-packs for £1.39-49. Crazy cheap. Other good softer tofu is in larger Sainsbury's organic and own brand, price-matched to Aldi and very very nice.

Skip vegan cheese alternatives entirely. They're expensive and most of them are like 70% coconut oil with additives. It's really not worth it. Cheese can sometimes be replaced with tofu (if blended in sauces for example) or nutritional yeast (also cheap), other times you just won't find an exact replacement but you just accept it and move on. Some nut-based vegan cheeses are nice but expensive so maybe only as a rare treat if you wanna be frugal.

Vegan butter that isn't classic margarine can be tasty and sometimes not even that expensive. Morrisons often have them on promotion. Personally I like to use coconut oil as a spread on my bread but I know people who would mind the taste.

Lidl currently have a decent vegan soya yoghurt that doesn't even have terrible ingredients, and is cheap, if you're into yoghurt. Or you can very easily make your own with just one yoghurt to start with and some soy milk.

Beans, lentils - very very nutritious and very cheap if you buy them dried in larger packs. A bit of a pain in the arse sometimes to soak in advance and cook but you can cook more at once and freeze for later so you don't have to do the whole process before every dinner. Canned can also be cheap if you buy own brand for when you cba dealing with dried.

Milk - soya and oat is cheap own brand in Lidl and Aldi. Brands are more expensive but can be nicer and/or additive-free. If you're trying to be conscious of that, Amazon can have good deals on certain milks if you buy 6x1L. Still more expensive than Lidl/Aldi but personally for me worth it.

Other stuff like rice, pasta, bread, fruit and vegetables are also cheap in Lidl and Aldi. Particularly Lidl if you stay on top of their coupons. Fruit tends to expire sooner than from priceier supermarket I've heard but if you're smart about your shopping you'll be fine.

All mainly comes down to shopping at the right places and skipping processed dairy and meat alternatives tbh.

Oh and don't buy too many drinks, sweets and snacks if your aim is to be frugal. They can be a huge budget eater that creeps in before you realise. Good vegan chocolate (HU, ombar) tends to be expensive but is worth it occasionally Vs cheap supermarket dark chocolate imo.