My "back of a fag packet" calculations are on post #17.
The situation for an average one vehicle owner/driver doing 12k per year at 50mpg = £240 gallon.
A nominal £240 road tax can be re-couped at 22.5p / litre fuel duty (assuming one pound divided by 4.45 litres per gallon)
Unfortunately, I know a few low pay care workers who do well over 12k per year as part of their contract to use personal transport to travel between clients, and pay for their own fuel costs (with a mileage allowance).
An increase in fuel duty would take a very large percentage of minimum wage care workers off the streets.