I find my food budget hasn't changed much at all. If anything it's gone down a bit.
I rarely use expensive unusual ingredients apart from chia seeds which I use go make a cheap and easy dessert. I don't bake low carb cakes but then I rarely baked normal cakes. I don't use much cream either - probably a small carton once every couple of weeks. The things I buy more of are cheeses and nuts.
I've found there's a lot of things I no longer need to buy and the savings on those more than balances out the additional things I do buy that I didn't before. Once a month I shop around for stuff like olive oil, coconut oil, toiletries, etc, and tend to bulk buy when I find a bargain. Try shops like Home Bargains, B&M, Jack Fultons (good for fish), Lidl, Iceland and Aldi.
In my house we tend to eat the same things as each other but with Mr C having a helping of some kind of carb on his plate as well.
I work to a tight budget so I make a weekly menu making sure to have mainly inexpensive healthy meals in the week and slightly more expensive healthy meals at the weekends, then I make a shopping list from that menu and either order it on-line from Asda for delivery or get the bulk of it from Aldi.