I would suggest that the problem is not so much uncontrolled airspace per se as the mixing in uncontrolled airspace of civil transport aircraft, military training traffic and unpredictable VFR private aviation.
Not many countries cram quite so much traffic into such a small space as we do in the UK. In the USA it's very easy to keep the military stuff away from the main routes. Where it does mix, in general all types of aviation are controlled by the same unit so there are not the same problems as here with lack of coordination between military and civil controllers.
Does anyone know if anything came out of the Shairspace series of meetings that happened last year?