Putting the charge on fuel duty is a little oversimplistic
There are a number of issues that need addressing with respects to car use, but it boils down to two separate issues: physical and environmental impact of the traffic.
Physical impact is things like congestion, but also things like wearing the roads out and so on.
Environmental impact is mainly the CO2 bit but also the impact on quality of life [for those outside the vehicle].
A blanket rise in fuel duty wouldn't resolve these, it would work out at something like 10p per litre (12000 miles a year @ 35mpg = 343ImpG= 1560 litres. Given a typical car tax of £160 that is about 10p a litre - your maths may vary) but it would be collected blanketly across all road users - this would not be fair for a number of reasons:
Rural drivers cause little congestion and in general little environmental impact above the pure CO2 output, however city drivers cause a much higher relative impact.
Conversely, sporty cars tend to have big engines but be fairly light, with big tyres - causing much less damage to the road surface than heavier but more efficient cars.
What would be fair, is to charge for road use based on a number of factors: vehicle size, weight and number of passengers, fuel consumption, each particular bit of road driven on and the time the driving was done.
Clearly this is very complicated, would require GPS tracing of every car coupled with cameras everywhere for when the GPS units "fail" (privacy anyone) and would be very expensive to implement, run and enforce.
Personally, however I favour a levy on fuel - it may be unfair but it is easy and, except for using red diesel, pretty much impossible to evade.