What most folk here who are what you call 'doubters' seem to be agin is the idea that segregation is either the only answer to safer cycling or that it is the highest priority answer to safer cycling. It has its place. As does control of traffic speed and volume. The roads, without the traffic are fine for cycling, therefore the roads are not the problem the traffic is. Presumed liability would bring about behaviour change in motorists but it is a crazy idea thought up by foreigns and therefore intolerable to the British publc.
Decent segregated facilities alongside certain strategic NSL dual carriageways, where no realistic alternative route exists (local example the A24 south of Horsham) may feel like a good starting point even to a doubter like me. I've seen Field of Dreams though, and what works with ghostly baseball players in a corn field is, I fear, unlikely to attract enough folks out of their cars and onto the segregated facility to justify, in the eyes of reasonable members of the general population who I'd be asking to pay for it, the huge cost of building it.