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You won't necessarily have to rewrite the highway code, or indeed the Road Traffic Act. There already exists provisions in the RTA to prohibit cyclists (and other non-motorised vehicles) from roads. Examples include sections of the A57 in Sheffield, sections of the A55 in North Wales and the A12 and the Strand Underpass in London. Of course all of these are proportionate to the environment and risks to vulnerable and/or slow road users. In each instance an appropriate alternative exists.
The test then exists as to whether these provisions can be applied to a multitude of other roads. TfL as a responsible authority for roads, could simply exercise use of traffic orders to prohibit cyclists from using the roadway and, in the absence of any other facility, cycle lanes would then be the only remaining legal option. Of course these orders could be challenged but then it would come down to who could make the best argument in a court of law.
There's a topic about this.
Don't think it'll happen unless you rewrite the Highway Code.