"put a sort of tax on cycles, lets call it a road tax"
They'd also have to have some sort of identification to tie enable TPTB to check tax is paid, let's call them number plates.
As a useful by-product we'd them have something of a handle to identify the very few (!) misbehaving cyclists.
And whilst we're about it, how about compulsory insurance, cycling tests and cycling licences so that cyclists would be under the same sort of regulation as drivers.