I really am annoyed at the way the media has gone out of its way to brainwash older people into believing that they have to choose between 'heat and eat' this year.
People on the state pension, whilst definitely not having money for any sort of extras, should be able to do both comfortably. If they are on the lower pension (and have no other income whatsoever - private pension etc), then they should be claiming Pension Credit. If on the higher pension then that should allow them to keep their home properly warm and to eat home prepared good meals.
Obviously, if people have extras like, running a car, smoking, foreign holidays, having a pet - then that is where they are choosing to spend their money. That is down to them, I have actually had people tell me they would rather be really cold in their homes in the winter so they can get on their cruise ships holidays in the summer!!!!!
If people have such large old properties that they find them difficult to heat then they really should have 'future-proofed' a long time ago. Understand people do not want to leave their life-time homes, but they do need to understand that it is costing them more by letting it get very cold each day and heating it up for the evening. A basically warm home all the time, is better for them, better for the property and better for their bank balance.
I would agree that our pension in UK is far too low - should be tied into Living Wage, but I really challenge the idea that pensioners are unable to heat their homes properly. We know that older lungs (as do very young ones), need around 18 degrees at the least.
Think the first thing the OP needs to do with their neighbour is to point out that their way of heating is probably costing them more than if they kept their home at a basic rate, and it is probably not as much as they fear to do so. If they are that hard up then they may be entitled to other benefits which they need to claim.