Progress report. I bought City Navigator and, using Basemap, have plotted my routes by placing two waypoint markers, one at the start and another at the destination, and then drawing a line with the appropriate tool and asking Basemap to plot the best cycling route.
I thought I'd better try this out locally, and was rather perturbed to find it directing me into some bushes at one point. I think there may have been a bridle path at that point but, as I'll be heavily laden on a road bike, I'm not really interested in off-road excursions. Like I say, a little worrying. I've decided that I'll take some maps along as back up (which is probably a good idea anyway.)