Have a read of the work by John Franklin on cycle paths, injuries, Milton Keynes's redways, cycle farcilities in other countries...
http://www.cyclecraft.co.uk/digest/sustrans1.html
http://www.cyclecraft.co.uk/digest/2decades.html
http://www.cyclecraft.co.uk/digest/redway.html
http://www.cyclecraft.co.uk/digest/research.html
It becomes very clear that separate farcilities do not make cycling safer. They can and often do, increase the real level of risk. Nor do they encourage cycling to any great extent.
When I was a kid, the mindset was only little kids cycled on the footpath. Cycling on road was part of 'growing up' and being a 'proper cyclist'
What is needed is not separation of cyclists from roads, what is required is more education of motorists to make it clear that actually, no, when driving you do not actually own the road, but you are sharing it with others, be they other motorists, cyclists, horse riders or pedestrians. But hey, that actually requires a lot of effort and time. Much better to go with the 'quick fix' of getting those pesky cyclists out of the way. The roads are dangerous, don'tcha know. Actually, for the most part, the roads are not dangerous. Cycling is a remarkably safe activity and has lots of benefits to it as regards human health and also to the environment. And it's *fun*
Having cycled throughout the UK and in France, Germany and Italy, our roads are not too bad at all. Yes, there are problems now and again, but cycling assertively - not aggressively - pretty much stops problems happening most of the time.
The other thing is, nothing in life is 'safe' Life is a risk - part of life is learning how to deal with risk. The risks of cycling on road are, IMO, greatly exaggerated and Sustrans emphasis on 'safe' and 'traffic-free' routes over emphasizes the risk level of cycling. It's another reason why I do not like Sustrans.