Sure, sure, let's make all the cheap foods even more expensive.
We'll make the expensive foods magically cheaper though. Right? Oh, wait...
Poor people are not all time rich. Plenty of them are financially poor as well as time poor. They cannot buy a bunch of fresh ingredients (cannot afford them) and cook into some nutritionally balanced meal (don't have the time, also might not be able to afford the cost of cooking, and might not even have access to kitchen facilities if living in temporary accommodation or homeless).
You're also forgetting that not everyone even knows how to cook, beyond shoving things in an oven and hoping for the best. I don't know about you, but I didn't get any cooking lessons at school, and I didn't get any from my parents either. If I didn't like food enough to figure out how to make it, I wouldn't know how to fend for myself in a kitchen.
Then don't forget all the 'picky eaters'. Some are picky. Some have allergies and only eat their safe foods, and some have ARFID. How quick do you think it would be for either group to get diagnosed and get help from the NHS?
Let's circle back to allergies. Shall we ditch this product for this nutritionally balanced one? Oh, wait. It has an allergen in it. Not everyone's allergens are one of the 'main' ones, so there's loads of tedious ingredient reading, and the need to buy brands you don't really want to, because they're the only ones you can eat. You don't get extra help for living with allergies. Some people used to get certain foods on prescription - that's been done away with in most of the UK.
If you actually care about poor people...
Cut VAT on their essentials like food bought from the supermarket.
Increase the personal allowance for people with diagnosed medical conditions like allergies, coeliac disease, IBS etc so they can afford to buy food that won't make them sicker (bonus effect: will reduce the strain on the NHS by tackling the source rather than the symptoms).
Improve access to NHS doctors and dentists so it is not impossible to register, they can actually be seen, and there aren't loads of hidden costs (bonus effect: preventative medicine can be cheaper than treating when things have already gone to shit, and by investing more in our NHS services, we might retain more good clinicians).
Scrap the cost of prescriptions throughout the UK (bonus effect: again, it's preventative).
Provide basic cooking lessons in school using cheap ingredients (apart from giving people more options in the supermarket, it might reduce obesity and again, that's a win for the NHS).
Provide more tax relief/benefits to the working poor so no one working needs to use a food bank to survive. (No one should need to use a food bank at all, but it feels even more ridiculous that some people who work genuinely do have that level of hardship.)
None of the above appeal? Oh, sure. Let's just tax their food even more. In a cost of living crisis. That makes total sense.