Yes, this is a problem, and I'm lucky in now having a garage, and when I plan my next supermarket run early next week, I will be doing it before I need any of the contents, and I will be leaving the bag and its contents in the garage for 72 hours, and spray distinfecting the plastic frozen packets before taking inside.
Funnily enough, I was reading advice on the BBC website this afternoon, giving more or less the same advice.
This is much more of a problem if you are a city dweller and have to go out every few days to get food and essentials.