I find it more expensive because:
I don't eat red meat apart from a little bacon/ham occasionally
my other health conditions make it hard for me to cook, I can only stand for a sort time and can't chop veg easily so I have to buy pre-prepared veg (such as onions) and salads
even after my gallbladder was removed I struggle to eat eggs - one a day max.
I end up buying some ready made salads, ready to cook veg and fish - plus occasionally, for a bad week, ready cooked chicken - so even without coconut milk, flour and almond flour that all works out a lot more than my old food list.
So eating low carb can be as cheap, or cheaper, if you have access to decent shops, are a meat eater, can spend time in the kitchen doing extra cooking/clearing up - but that doesn't work for everyone.
TriciaWs - Whilst I am fortunate enough not to have health issues limiting my ability to spend eons of time in the kitchen, sometimes my lifestyle ramps up and I find the time the issue. I don't have hours to slave over a hot stove.
On that basis, I tend to batch cook, ad often, if I have the oven on, I might lob a chicken in there, in whateverrr format takes my fancy - whether a straightforard roast bird, or spatchcoked and spiced, or whatever, it'll mean as well as the meal being cooked, I have several meals from the chicken. When cooked, I'll then cut it up - legs, wings, brasts, for whatever, then reserve the bones to make a delcious meaty stock (a couple of hours of decent ignoring on the hob, or less in the pressuree cooker).
I popped into ASDA yesterday afternoon, just after 3pm and grabbed some diced swede and swede and carrot (which I can tolerate), reeduced to 10p a bag. In the other reduced area there was lamb mince, under £1, pork loin chops, 40p and a lamb chump roasting joint under £2.
Whilst those may not necessarily all be things you eat, I guess I'm suggesting things can be helped by being flexible on batch cooking and being opportunistic with butcherry/fishmonger bargains. Of course, the yellow sticker products shouldn't linger too long in the fridge beforere cooking or freezing, but with a freezer, it adds to the option.