Road tax was abolished 74 years ago. Road tax doesn't exist. It's car tax, a tax on cars and other moror vehicles, not a tax on roads or a fee to use them. Motorists do not pay directly for the roads. Roads are paid for via general and local taxation, which almost all of us pay. In 1926, Winston Churchill started the process to abolish road tax. It was finally culled in 1937. Car tax (or Vehicle Excise Duty VED) is based on amount of CO2 emitted so, if a fee had to be paid, cyclists would pay the same as 'tax-dodgers' such as disabled drivers, police officers, the Royal family, and band A motorists, ie £0. A lot of cyclists are also car-owners, too, so pay VED.
I'll get onto the rest of your post once I've had my toast.