They had £317,000 so either Hermionie is secretly rich, she stole from her parent's accounts, or someone else prepared cash while Rowling thought the reader assumed it. They have to be in the wilderness most of the time on the run and all that. However they weren't averse to going to town and buying food, they did it for a special occasion (I don't remember what) but the stupid thing is that they never thought to keep buying food.
A summary of what she was thinking is that they weren't going to be driven out of Grimmauld Place. So she decides to bring what was needed for their infiltration. The book never mentions their escape plan, I'm assuming whatever it was doesn't work once caught. They were NOT in the same position as a resistance, their situation is more like fugitives. She also probably brought tea to relax themselves in a tense situation and in the wilderness it doubled as heat and hydration and YES British stereotypes.
As for the cheap excuse to make everyone hungry: yes, but consider they didn't think about being busted. Also people tend to forget about food when being fed by someone. So remembering to bring tea and not food is not out of the ordinary. One might wonder why they had so much cash if they were so short sighted. It's easy to assume someone DID go to the bank off page for some spending money that afternoon and just hit "zero" too many times.
As I mentioned they DID buy food at one point. However it was a small shop possibly family owned. These tend not to have a lot of preservable foods like canned food, at least in my country. I think going to buy food more than once a week, even at different stores, is going into settled areas way too often considering that would look like vagrants who just happen to look like wanted people. Without access to refrigeration, there isn't much from the smaller shops that won't perish too quickly.
One could argue that after they bought food once they could consider buying food every week to relieve their foraging pressure. I don't really have a rebuttal to that. Maybe they just didn't have enough time to think?