I know this might sound like pedantry, but I think it important. There is plenty of room on nearly every UK road to have full cycle facilities. After all most roads accommodate at least 2 lanes of traffic, often with parking and chevron dividers in the centre for right turns etc. Many major trunk roads, even in cities, are multiple lane affairs with large junctions.
What we (we as in society) have decided is how to divide this road-space up. And the collective decisions over years has arrived at the current situation.
Don't get me wrong. I don't particularly want every road to have segregated paths for bicycles - not least because it is unnecessary on many roads which could be treated to simply reduce speed / through traffic, and it is politically unacceptable anyway. When we have pathetic cycle facilities such as the one in your link it isn't because there isn't space for something dutch like (just look at the number of car lanes!); it is instead because we would prefer to use the space for cars, traffic engineers don't understand how people ride cycles, and don't prioritise cycling facilities. The reason that we have so many of these white line "facilities" is that it is easy to measure and cheap to install and they can then pretend that they are cycle friendly. My own council boasts of x miles of cycle lanes in the borough - neglecting to mention the quality of said cycle lanes.