In London we simply don't have space to put in dedicated cycle paths everywhere. IMHO, they're treating the symptom anyway, the problem is that a large number of road users in the UK (including quite a few cyclists) are aggressive, discourteous or just plain bad drivers/riders.
Cycle facilities (cycle lanes - dedicated or not, off road cycle paths, advanced stop line boxes, etc) all help encourage people to cycle; this is great as the more people on bikes on the road the safer it is for everyone (see TFL's "Safety In Numbers" campaigns). But a 2mm high strip of white paint on the road isn't going to save me from an idiot that is texting whilst driving and not looking where they're going. Ideally we wouldn't need any on-road cycling provisions at all.
I've ridden a bike quite a bit in France and have had no problem with the car drivers there, they give plenty of space when overtaking and have no problems being temporarily held up behind a cyclist until it is safe to overtake. No special facilities, just courteous drivers.
Segregation works both ways. This is anecdotal, but on one long distance ride in the UK there were sections where the riders were overtaken by the support vehicles of other riders (mainly the european riders). By far the worst (in terms of least distance given when passing) for overtaking were the cars with "NL" markings on their european number plates. My guess is that the years of segregation have put them out of practice with sharing the roads with cycles. Again, that's just my experience.
FWIW I cycle commute almost daily in London (I took the train today as I've got a horrible cold) and have grown used to London traffic. The closest times I've come to an accident were all my own fault. I've read "Roadcraft", I've had a full driving license (both car and motorcycle) for 15+ years, I did do cycling proficiency at school, yet I'll still take the opportunity for more training if it comes up (the local London boroughs to me often provide free cycle training every so often). I don't undertake vehicles approaching left turns, or overtake vehicles approaching right turns. I avoid cycling in the 'door zone' and I'm especially careful passing stopped cabs as the doors are invariably opened by passengers without looking. I'll be assertive but not aggressive. I smile at the lemming pedestrians that walk a step or two out into the road before looking. etc.