There's no such thing as road tax, roads are paid for out of general taxation [0]. What they're thinking is vehicle excise duty, which doesn't apply to all vehicles, so that point is moot.
I would assume drivers are also thinking of the fuel tax they pay, not solely the excise tax. The UK has some of the highest rates of fuel taxation in the world.
Which is something you pay, at least in abstract, for someone else to clean up the carbon dioxide you litter the atmosphere with. If you dpn't want to pay the cleaning fee, don't litter -- take the bike!
Is that same level of tax levied on heating oil? If so, that bolsters the case that it's a carbon tax. If, as in the US, heating oil is untaxed or is taxed at a fractional rate of automotive fuels, that suggests that it's a road tax and not a carbon tax.