If the problem is the poorest, why not use the fuel duty raised to help them? They're surely not using all the fuel, so this could be a net benefit to them.
The problem I have is that those incentives are driving people to kill themselves as they cannot afford to live anymore. I guess that's what the government wants though, less pollution.
Can't pollute if your dead.
Better yet to build electric vehicle infrastructure (trains, trams, charging stations - cheap compared to housing) which could also be used by some business, tax non-train freight. Replace buses with electric ones.
Farming cannot be done in the middle of the city and you probably do not want factories there either... Your move would likely kill the remaining parts of this business if successful.
Which is why I added the other paragraph.