As well as incomes I expect age profile I would expect to have an influence too on death rates. A lot of deaths are in the over 50s and the older the more deaths. Ethnicity, general heath including obesity also seem to be factors that could be related to high death spots. Teesside figure look as predicted to me (taking account of lower incomes and urban nature), but it is a bit unbalanced, why should Middlesbrough have so many more deaths per capita then Hartlepool?
Having said all that rich people can suffer, look at Boris Johnson who is wealthy probably in the top 1%, lives in posh areas, he was really suffering, but you could say he did not die, but may have if he was poor.