Well, my Mum has certainly started drinking and smoking more sonce her income dropped. It seems to be stress and boredom. If you are at work all day you have to wait for a break and go outside to have a cigarette you are aren't as able to smoke as many cigarettes as if you at home. With alcohol, you can drink more at night because you dont have to worry about getting up and driving and going to work with a hangover the next day. Free time gives people the opportunity to indulge in bad habits. Even if you didn't increase people's income if you kept them busy I think there would be health improvements. Take the obesity epidemic- some of that is caused by sedentary office jobs but they may still burn more calories than someone at home all day. Unemployment is also often a cause of depression, which then can lead to these other probelms above.
However a lot of health problems have their seeds sown in utero. Parents need healthy lifestyles so they can pass these good habits onto their DCs. I think that, at the extreme end, education has a lot to do with it. In some deprived areas 25% of adults are functionally illiterate. They cannot read health education posters or leaflets. They cant read newspapers. They have never used the internet. They cannot read the ingredients or nuitritional information on food packaging. They have never heard of BMI, or know how to calculate units of alcohol, or know what vitamins and minerals are in what foods and what each does. They dont know what causes heart attacks or cancer or strokes or diabetes. They dont have the numeracy skills to calculate a food budget.
I think it is difficult for middle-class well-educated policy makers to understand this. They assume 'everyone knows this stuff' but sadly they dont.
There are also geographical issues at play here. Lots of children are very sedentary, which is a health timebomb. But poorer children's opportunities for activity can be much more limited than their middle income counterparts. Eg- They may live up a tower block and not have their own garden. Their parents may be too depressed/obese/drunk to take them to the park. They cant afford to go to soft plays/after school sport clubs or a bike. Their parents may feel that the area they live in isn't safe enough to allow them to play outside. Some health problems (like asthma) are directly linked to some of the dreadfully poor housing stock that some families still live in. Damp is still a problem in many buildings. Some buildings have very thin walls, making it easy to be disturbed by noisy neighbours late at night, disturbing sleep, which is essential for good health. There are 1000s of families living in overcrowded conditions which causes stress, which is often behind lots of physical health problems. In some neighbourhoods there are no shops selling fruit or vegetables. They are an expensive bus journey away.
Then there's the insecurity of a low income lifestyle. If people are stuck in the private renatl sector they are likely to get moved on every 6 months. This may limit their ability to stay on local waiting lists for servies like dentistry, physiotherapy etc. If someone has found themselves homeless and has to start from scratch with no possessions they are going to find it difficult to prepare a proper meal with no or few utensils or basic kitchen equipment. This also applies if they dont have suitable clothing for exercising in.
Oops, didn't mean for that to turn into an essay.