When I was at my most skint, I used to eat a vegetarian diet, not through choice but through poverty.
It is most definitely cheaper to eat a vegetarian diet, so long as you have some basic cooking skills.
I used to buy unbranded dried soya protein from the health food shop (essentially quorn) which you rehydrated with boiling water (or kwik save stock cubes) then used like mince. It was dirt cheap.
I also bought things like kidney beans (dried not tinned) again dirt cheap, but a bit of a faff. You need to soak overnight, then boil for forty minutes before use.
Lentils, chick peas, various dried pulses, all dirt cheap.
Rice, again cheap, if you buy unbranded in bulk, not uncle bens "easy cook" which personaly I find amusing. Is there anything easier to cook than rice? I mean, chuck it in a pan of water and boil till its cooked. The world is full of morons.
You know, sometimes I'd live on nothing but rice for weeks on end due to needing to pay bills (thank you Yorkshire water, & especially for that lovely "oh you can't pay this months installment, well we'll make you pay for the whole year then, in advance" policy).
Sorry, that turned into a rant.