It probably varies a bit from country to country and whether not you live in a climate that allows things to be grown all year round and the presence of farmers markets etc. or if you have to rely heavily on imports and supermarkets... BUT, for me I wouldn't say it's cheap, but it's definitely cheaper than eating meats and other animal products.
No matter what you eat/buy I think it is important to not waste food but to plan accordingly and to utilise things like your freezer to make sure that you don't have to constantly buy things fresh. If I have bananas that I can tell are getting very ripe and I know I won't have a chance to eat them before they go bad then I chop them up and freeze them to use in smoothies later, just as a simple example. I live on my own too and I make sure to always bring packed lunches to work and that alone keeps down costs and when I go grocery shopping I always have a list that's based on my meal plan for the week and I don't go off track in the shop. I stick to my list.
I would estimate that I have cut my food expenses in half since I went vegan, but that's not only because of what each item costs in the supermarket, but also because I notice how I eat out less often, cook from scratch more and snack less. All of those things contribute as well, but where I live anyway, even meat substitutes are still way cheaper than getting actual meat.
