Sustrans if you didn't already know is the co-ordinator of The National Cycle Network. The network offers over 12,000 miles of routes on traffic free paths, quiet roads and traffic calmed roads. They also claim that 75% of the UK population live within 2 miles of a route. How good is that!?
Having used the network, the boys and I are regulars on these routes, we have found all the routes to be well signed and connects to towns and villages very well on pretty safe roads and paths.
Try and find a route near you at SUSTRANS
If you explore their site you can also find a section with routes posted by other users for your local area. A very good resource for finding new routes for your training or family bike ride.