> We tax gasoline because it has negative externalities (same as us taxing cigarettes and alcohol).

This is contradicted by the difference in taxation for diesel fuel and heating oil (which is also the case in the US as well). Or used for generating electricity, as you point out.

I think that like many things in government, there are multiple reasons for taxing gasoline; negative externalities is one of them, but acting as a proxy for usage fees is another.

In the US at least, the federal gas tax is specifically earmarked for transportation expenses (https://en.wikipedia.org/wiki/Highway_Trust_Fund), which indicates that it's explicitly intended as a proxy for usage fees.

> Until relatively recently that's not really been possible (ANPR makes it possible), hence taxing fuel as a proxy.

Yes, but times change, and it is possible now. Lots of people bring up the problem of not collecting gas taxes to fund roads when electric cars usage grows. So every time someone brings that up, I suggest a fairly simple solution. Electric cars also weren't previously possible, but they are now, so rather than complaining about how we won't be able to fund the roads, how about charging more effectively for road usage.

> Given that the cost of a road is wear and tear (which a pedestrian or bike causes pretty much zero)
>
> Charging more than £5 a year for even the most extreme cyclist wouldn't make any sense.

I addressed this in my comment, indicating that it doesn't make sense to charge usage based amounts for cyclists:

> while a bicycle uses so much less (and pretty much equivalent to any use of public space like walking, using a scooter, etc) that it makes the most sense for that to just be accounted for out of the general fund.

There is the cost of constructing the roads in the first place, and wear and tear from weather, but that can be adequately accounted for out of the general fund; and when I say that, I mean the taxes collected at whatever level of government is responsible for paying for road maintenance that are not based on road usage at all, such as income tax, sales tax, VAT, property tax, or the like.

As someone who lives in the Northeastern US, I know very well that it isn't just vehicle weight that leads to road wear and tear; I've ridden on dedicated bike paths that were unmaintained, and frost heaves and roots of trees cause quite a lot of trouble, though it does take a lot longer for it to become unusable than roads used by cars and trucks.

Anyhow, I think we're mostly in agreement here. It is absolutely possible to do more effective taxation of vehicles based on their direct costs to infrastructure as well as other externalities.

> Because damage increases at 2^4, 1 mile car does about 1/100,000th of the damage of a lorry. A bike and car is a similar ratio - therefore if you charged a bike 1p per mile, you should charge a car £1000 a mile and a lorry £100 million a mile.

The damage per axle is proportional to the weight per axle to the fourth power. You multiply that by the number of axles to get the total amount of damage. Also, tandem axles do substantially less damage than single axles. This ends up at being a factor of about 5,000 between a passenger car and a truck, not 100,000.

It's still a big difference, and it's not accounted for by gas taxes, tolls, or vehicle registration fees, at least in the jurisdictions I've checked. Most of them seem to just go up proportional to the weight or the number of axles, not the fourth power of the weight per axle.

If you want to do it right, you'd charge fees based on equivalent single axle load times mileage, plus a congestion factor in congested areas based on the area taken up by the vehicle, times the amount of time it's within the congested area, times a time-varying congestion factor. And of course a carbon tax which covers all forms of carbon emission, and possibly a particulate emission tax that varies with density.

But despite how obvious it all sounds, it would be somewhat expensive to implement, and would face huge political opposition from industries and individuals who are effectively subsidized by paying into the highway systems way less relative to their usage than other users.