Many European countries (Swiss, Austria, Hungary, Slovakia at least) have a vignette system. You cannot use a Motorway or major road without buying a vignette, Most countries allow you to buy them for a few days, weeks or a year. Both locals and foreigners have to buy them, and there is a fine if you use a motorway or dual carrageway without one.
But Auntie Flow who only drives to the shops and church once a week using local roads doesnt need one, so it doesn't cost her any more. Any locals that use the roads more buys a yearly one.
My proposal would be to half the current Road tax price, and introduce a vignette for all motorways and non urban A trunk roads, which would cost the same as the (new half price) tax disk. Then legislate so that all cars (foreign and local) had to have a vignette to use the affected roads. That way you can collect 'road tax' from foreign lorries and cars, unless they really want to try and drive from Dover to Scotland and back on urban and B roads.