The UK National Cycle Network provides over 10,000 miles of cycle routes throughout England, Wales, Scotland and Northern Ireland. The routes comprise a well signed network of traffic-free paths, quiet lanes and traffic-calmed roads, although care must be taken because quiet lanes seem to be an attractor to 4x4s!
Sustrans is the co-ordinator of the scheme and they offer
interactive mapping which displays cycle routes local to a given postcode or town name.