AFAIK there are two approaches to downloading maps. On my iPhone OS App:
1. If you tap the 3 bars then Routes, then choose a new route it should say "Map available to download" at the bottom of its panel. Then tap the adjacent down arrow and the tap Download map. The app will automatically determine a rectangular area of map tiles which contain your route at all map scales and will download these to your phone either via a WiFi or mobile data connection. If you have an adequate connection to the OS tile server, you should see the the download complete fairly quickly. If the connection is poor/broken it will pause, but will let you resume if the connection is restored. So far, the only problems I have had with map tile downloading have been when my internet connection has dropped out.
To visibly check which map areas you have cached to your phone, tap the 3 bars then Offline Maps, then tap the slider next to "Show offline areas on map", then tap the < button top left , then Close to go back to the map screen. The areas of mapping that are cached are coloured green. Incomplete downloads are in grey. Pan and zoom the map to see where the green area are.
To check the list of cached map areas, tap the 3 bars then Offline Maps, then tap Custom offline maps at the top. Successful map downloads have an orange bar. The > panel can be tapped to see the downloaded map area (which will be tinted green if you enabled this as above). Back in the list of Custom offline maps, you can be tap to remove map. Failed or incomplete downloads are shown and have a grey bar on the left and can be tapped to Download map. The list can be edited by tapping Edit and selecting maps for removal to free up memory if you need to.
2. The second way is to tap the 3 bars then Offline Maps, then tap "Add a custom offline map". Pan and zoom your map to display the area (i.e. full screen) that you want to download - this can be a portrait or a landscape rectangle depending on the orientation of your phone. When finished selecting the area, tap Download, then give the area a name and tap Save at top right. This area of map tiles will be saved to your phone memory. Check as above before setting out on the hill.
Hope this helps ...