The National Byway
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It runs along quiet roads, rather than a mixture of roads and tracks like the National Cycle Network, making it more appropriate for road bikes.
TODO interactive online app? Ahh, those charities that try to make money by individual transactions... when they die, nothing will be left of all their work.
Edit: noticed that it is on by default on OpenStreetMaps web UI under the "Cycle Map" layer marked at "NB".