Google Maps download offline maps. This works very reliably, you can select the area you want to download. The only downside is that Google maps can't reliably show a route offline, and it does not contain national cycle route routes. Or those features are impossible for a software engineer to get working after trying for about 2 hours.
OpenStreetMap on browser with cycling layer: www.openstreetmap.org/#map=5/49.582/1.934&layers=C This is the best visualization of cycling routes I've found so far, contains both National Cycle Network and National Byway and a few others, and they are shown extremely clearly. But as a website it doesn't reliably work offline
the OsmAnd app for Android is the best offline free-ish OpenStreetMap viewer I've found so far. You only have to pay after reaching 5 region downloads, and it is very cheap if you want to do so. The cycle route view is not amazing, the routes are not so clearly marked and mixed with very similarly colored big roads, but with a bit of effort you can make them out. No routing though
I've heard Komoot can keep a predefined route (possibly auto planed) reliably offline, but haven't used it myself. I was not able to see National Cycle Route clearly marked anywhere on it

The best cycling map app

 Ancestors