Externalities estimates like that are notoriously fraught and depend on value judgements that are not at all simple to make.
It doesn't help that these estimates are almost always done by people with a pretty clear agenda.
(I do this sort of analysis for a living, but ultimately I am not sure I really trust any of them beyond the broadest strokes).
One factor which is fairly reliable is the £15bn cost of road accidents which the government quotes in some of its documents.
Whilst that still leaves about £15bn before you reach the limit of the raised taxes, there's quite a lot of factors which would quickly erode that. Of course, how quickly and how far is still up for debate.
One thing which is worth noting is that there's also a lot of private money which is spent on roads (almost all from developers to mitigate traffic from me developments), as that impacts on build costs and often funds things which should be delivered by councils it muddies the calculations. As is it extra tax income (although often it's spent directly by the developers) or should it be spending which should be counted as a cost of government (at whatever level), should it actually just be a building tax so that it could be used to build bigger projects (for example it's it better that over a 15 year window 1 million homes are built with a cost of £5,000 worth of small schemes (probably quite a lot would be spent on fairly minor improvements like upgrades to bus stops) from each house, or that money (£5bn) is used to build Crossrail 2?
The other thing to consider is that it'll be impossible to have no railway without a significant change to the life of vast numbers of people (even those who don't use trains), even if it were possible the cost to make the required changes would make the cost of running the railways look cheap. It would also require a LOT more land, which then becomes a problem as everything gets spread out to provide the required parking, which makes walking and cycling harder, so even more people drive.
A small increase (even +20% would likely be less than £100 a year for the majority of people as on a fuel bill of £900 per year it's an extra £60, but given that car ownership is £3,800 a year as a percentage of that total cost is quite small - and again at 20% uplift that's quite a lot more than any would be suggesting even over the term of the parliament, and it probably wouldn't need to be anywhere near that high) on fuel duty is probably useful to do. Especially given that it's likely to not impact as many people as it used to, due to electric cars, and just the thought of an increase (even if the numbers aren't known) is likely to alter some people's travel behaviour.
For example it may mean that they walk a bit more, or they look to swap to an electric car. Both are likely to be useful, for example people being fitter and costing the NHS less and assisting with the move towards electric cars or making people look at the total cost of their car ownership and whether it's truly worth doing so.