I've ridden in much of southern England and have always created my routes using the RAC Road Atlas Britain that is 3 miles to the inch. While it doesn't show the Cycling routes, I have found that the cycling routes seldom go where I want them to go. The maps show all the A, B, rated and unrated roads in enough detail to select a route using the least travelled roads. The only place they breakdown is around major cities where there are too many roads to show at the 3 mile to inch scale. The cites are usually shown as an inset in another part of the atlas. I rip out the pages I need and leave the rest of Britain at home. Frankly, I find creating the next day's route one of the odd pleasures of touring in England.
Beside the lack of city road detail, the only other problem with using the road atlas is that it doesn't show much elevation. After while, though, you figure out that following rivers is flat and going perpendicular to them is up and down!
Have a great time!
Ray