I don't think for a minute that 'our' roads will be taken off us. For a start, to duplicate all routes nationally with cycle routes is just too costly and is never going to happen. It may be conceivable that some duplicate roads could become dedicated cycleways, and the parallel long-distance trunk roads could become non-cycling routes, but we already have plenty of those - but without the concomitant cycleways!
Even in an urban environment, unless you start from scratch, there will never be sufficient cycle-only routes to justify closing large numbers of roads to cyclists. However, if you take some of the space currently allocated to all traffic and reserve an adequate amount of it for cyclists, I see no great harm in the adjacent vehicle road being closed to cyclists.
One of the consequences of greater amounts of vehicular/utility urban cycling will be that there will have to be more give and take between cyclists; it won't be appropriate for people to ride as though they're training for a race amongst people who are bimbling to work in normal clothes at 8-10 mph. I foresee speed limits for cyclists!