I live in what is considered to be a poor area, lots of the local schools are in special measures, we have a larger than average amount of children taking up free school meals etc. Unemployment is a big problem, as is teen pregnancy, lack of suitable housing and lifestyle health issues like obesity and type 2 diabetes are a big issue. Families tend to be large, with single parents or unemployed parents or both.
I know this because they gave us a lovely talk about how unfortunate we are at the community centre one day 
I buy fresh fruit and veg but with DH working away in the week and just DS and I at home, things go off before we use them. I do my best with things I can cook and freeze, but what do you do with, for example, a cucumber that's passing it's best?
I have a car but many people don't. They are just too expensive a luxury
Anyway, the nearest farm shop is several miles away. It would take me about an hour and a half to walk to it, and I walk quickly. So that would be a three hour round trip to buy good fresh veg that was cheap.
Public transport would mean two buses there and two buses back and still take about an hour. I think you can buy an all day saver for £4.25.
In the other direction, the nearest market is about an hour's walk. It runs Tuesday, Thursday, Friday and Saturday.
It's only one bus each way but the fair is £2.20 each way from here, so still quite expensive.
DS was only in school in the morning, for three hours, last year so trips like those for people without a car are difficult if not impossible if they have young children not in full time school.
There's no way I could walk to the farm shop and back in time to fetch DS, and no way I could walk with him to it after school. That would add at least another hour to the journey because he's smaller, slower and he would need to rest more than I would.
And as we couldn't buy fresh stuff in for the whole week without taking the risk that some of it would go off before we'd used it, we'd need to make at least two trips a week to ensure we were buying the freshest we could get.
So that's the two places Jamie would prefer us to shop written off for many families here. Even if they don't work, the cost of transport or the time needed to get there and back makes it difficult to impossible in many cases because of children/school/childcare etc.
Within walking distance we have a Lidl, which is about a 20-30 minute walk for me. And an Asda about a 30-40 minute walk. Sainsbury's about 40-50 minutes away.
Within fifteen minutes I can walk to the local equivalent of Iceland for frozen meals. Or to Iceland itself within half an hour.
I'm not surprised that many local families do. I'm sure they already know it's not the healthiest food, but it is cheap and convenient in more ways than being microwavable. It's local, they can walk there and back in much less than an hour, it's cheap and freezable. If the market or the farm shop were closer they might be used by people local to me but time, travel costs and distance have put them out of reach on a daily basis for most if not all people here who don't own a car.
It's not just about people being too lazy to cook or finding the microwave more convenient.
Not everyone has a market or farm shop on their doorstep, and a three hour round trip every day to buy ten mange tout is a big thing to ask of someone who has young children to get home to before school is out.