The RACF's argument is based on these statistics from the ONS, showing that there are around 800,000 households in the UK who are in the poorest 10% of households according to disposable income and who own a car, and that these households spend an average of £45 a week on transport, including an average of £16 a week on motor fuel. As these households all have a weekly income of less than £168 (see the top row of the table) that means that many of them are spending more than a quarter of their income on transport. The RACF calls this 'transport poverty' and thinks the way to deal with it is to make fuel cheaper.
There are several problems with this argument. First, what the RACF don't tell you is that only 31% of households in the poorest tenth of the income distribution actually own a car, compared to 96% in the richest tenth (see p.9 here). So if 'transport poverty' due to fuel costs is a problem, it is a problem only for a minority of the poor.
Second, it is likely that many of those the RACF say are in transport poverty aren't really that poor after all. Households with very low reported incomes are often there because they have suffered a temporary drop in incomes, but they could still be otherwise reasonably well off. As these academics point out,
for some of those at the very bottom of the income distribution, a recorded very low income should not be taken as a sign of more general lack of resources... It might reflect the fact that some individuals experience very low income for a relatively short period of time, but that they maintain their spending at some sort of long-run level: for example, someone between jobs (who could have a 0 or very low income if measured over a sufficiently short period), or someone making a loss in their selfemployment business (which would count as a negative income).So it is very likely that many of the low-income households who own cars are only temporarily low-income. But even if we accept that these households really are poor in the usual sense and that enough of them own cars for this to be an issue (no matter how contradictory those two statements might seem), there is a third big problem with the RAC Foundation's argument. The ONS figures they cite indicate that car-owning households in the poorest 10% spend around £13m a week on fuel (830,000 households with an average weekly spend of £16), compared to spending on fuel by all households with cars of around £640m a week (19.7 million households with an average weekly spend of £32.50).
That means the households in 'transport poverty' account for just two per cent of total motor fuel spending in the UK. By contrast, car-owning households in the top 10%, who all have disposable household incomes of over £57,000 a year, account for 21% of total motor fuel spending. So any cut in fuel tax aimed at reducing 'transport poverty' would overwhelmingly benefit the better off.
Cutting fuel duty would be an extremely bad way to reduce poverty, especially if the money has to come from elsewhere. If cuts in fuel duty were paid for reducing benefits then you would be directly transferring money from poor to rich. If the RAC Foundation are really interested in reducing 'transport poverty' then they would be better off arguing for reductions in the cost of transport modes used mostly by the poor (i.e. the bus). But the best and most tried-and-tested way to reduce poverty of any kind is to just give poor people more money.