Bernard - I don't want there to be any unnecessary deaths. However you are guilty of an oversimplification (not just the fact that this is more about CO2 emissions than winter deaths).
Having a low energy efficiency does not mean it is impossible to adequately heat a home - it just takes more energy to do so. This will cost more, and those on a low income will struggle to afford it. It is that lack of affordability of fuel you are concerned about.
Private landlords could be forced to pay to improve their properties for the benefit of tenants on low income, and more vulnerable to the cold. Then you are basically creating another tax the landlord has to be burdened with for the crime of supplying a property that is expensive to heat. The fact that the tenant had the choice to rent one of their homes or not is quickly forgotten or dismissed. I do not think this is fair. A third party should not have the right to alter a lawful agreement entered into voluntarily.
It is every person in society who supports your view who should have to pay for this. How much will you sacrifice of your own earnings? Or are you going to tell me that only the landlord is responsible for knowing his tenant's income and circumstances?
Wouldn't it be simpler for individuals who are at greater risk of the cold, and on low incomes, to consider the EPC before agreeing to rent a property and take responsibility for their own wellbeing? Or alternatively, enter into negotiations with the landlord to include heating as part of the rent, so they will not get caught out in the winter. There are a number of options which don't incur expensive regulation and enforcement.
All this will achieve is rents going up over time, costs of enforcing the regulations, inconvenience and costs for landlords - which will probably cancel out the savings from lower fuel bills anyway. Terrible.