Is the lack of availability really the cause though?
It was said earlier that shops selling fresh produce in these areas aren't profitable, so they don't open - why aren't they profitable? Is it possibly because the local population don't actually want that sort of thing?
There was a TV program a little while ago where a celeb chef wanted to sort out school meals, introducing healthier meals properly cooked instead of heavily processed deep fried or microwave slop.
The kids complained, the parents complained - the parents even went to the lengths of passing McDonald's meals over the school fence to their kids because "they can't be expected to make it through the day eating that green rubbish".
So, said chef visited a few parents - showed them how to cook at home instead of relying on microwave meals and takeaways.
The parents complained about the cost (even when it was within a couple of percent of their existing budget) while stood in front of their 50" TV holding an iPhone whose monthly contract cost could feed a family of 3 for a week...
To put it into perspective - I have a shop and a chinese takeaway within a mile, the shop sells mainly frozen meals, not a huge amount of fresh stuff. The closest place to get "good food" is about 8 miles away.
We manage, and we're hardly wealthy.