The United Kingdom.
I've always been wary of riding in the UK because of the narrow country roads lined with hedgerows making it exceedingly difficult for riders to see oncoming traffic and for them to see you.
The UK has a mapping system called Sustrans that shows all of the cycling routes in the UK. In the past I could never plan a route in the UK because of the large number of the routes on the map that did not exist or where not really suitable for cycling. However, recently Sustrans has done a great job of culling of poor and unsuitable routes.
From the Guardian: "The National Cycle Network (NCN) will lose almost a quarter of its 16,000 miles of UK-wide cycling and walking routes from Monday, as part of an ongoing plan to improve safety standards." "The move follows a 2018 review by Sustrans, the charity that created the NCN, which found that 42% of the network’s routes were “poor”, with substandard crossings, signage or main road sections, and 4% “very poor”, taking cyclists on roads with heavy traffic. In addition, urban roads with speed limits in excess of 20mph and rural roads faster than 40mph are being taken out of the network."
The new and improved National Cycle Network (NCN) can be seen on OS Maps (Ordnance Survey Maps) Add the NCN layer to see all of the routes, click on the icon that looks like a book in the lower right corner (an example is in the map to the left). 
Orange lines and Orange dotted are traffic free. Using information found on OS Maps, one could plan a route across most of the UK on safe and mostly traffic free routes. This was a very difficult task until the mapping system was improved.
Cycling UK has area guides that are very good and maintain a list of cycling information called "Cycle A-Way" for each area. It seems to be very up to date and provides detailed information on each location.
British Air deserves a mention here because of their generous policy on traveling with bicycles. As long as your box is under 50lbs. you can ship your bike as your checked luggage without any additional charge, no oversize fee. BA sent our bike through as regular luggage, no wait at the oversize door at baggage claim. And we were first off the luggage carousel at Heathrow.
Guides, Maps and Other Information
Sustrans The primary transportation planner on the Internet for the UK. Similar to Swissmobile. "We're the charity making it easier for people to walk and cycle." Design and archive your own routes, Calculate their characteristics (length, height difference, longitudinal profile, travel time), Print routes Add texts and photos to the routes, and download GPS tracks
OS Maps Excellent mapping tool for the UK and other areas. "Discover hundreds of thousands ready-made routes at your fingertips. Simply open the OS Maps app and instantly start finding local routes nearby. You can also create and plot your own routes so you can explore the way you want to." Has some offline map capability if subscribed.
Cycling UK The area guides are pretty good on this site which covers much of the UK. They also maintain a list of cycling information called "Cycle A-Way" for each area. It seems to be very up to date and provides detailed information on each location.
Cicerone Cycle and Travel Guides Cicerone is a UK based publisher of travel guides, we have several in our home library. "Our expert and passionate team of authors, editors and designers work together to produce inspirational and detailed guidebooks, ebooks and routes to the world’s best walks and treks, mountains and cycle routes. "
National Rail and PlusBike We rely on national rail systems to get around with our bikes while traveling so here is a link to UK rail and their PlusBike info. about traveling with your bike on the UK train system.
See the Maps and Guides page for more mapping information.
England, Scotland, Wales, Northern Ireland, click for the UK's National Cycle Network maps. "The National Cycle Network is a UK-wide network of signed paths and routes for walking, cycling, wheeling and exploring outdoors".
OS Maps has an app for the NCN, however it is not an offline map. The paid version of OS maps allows downloading offline maps. The premium topo maps are not much better for bicycle navigation because they are too detailed for this purpose.
There are many cycling apps with maps available for phone/ android. Here are a couple of the better off line apps.
Can be used to follow this route (and other routes)
If you have a KML file of a route, place the file in the maps.me bookmarks folder (MapsWithMe/bookmarks on your phone or tablet) or alternately, email/text it to your device and open the file with maps.me. Total Commander works great for managing and opening files.
Guru Maps can show map types other than OpenStreetMap, in particular it will display OpenCycleMap. KML files can be imported by "opening" the file with Guru. Place the file in a folder or email/text it to your device, press and hold and open with the app. The route will appear in "collections." A user manual is available.
What the ride is like
The UK doesn't have any long distance routes that will take a person across the country, an example is Canal du Midi in France. They way we organized our travel was to find an area we wanted to see and then used the bike routes to get around the area. We started riding in Canterbury and then rode east along the southern coast of England. This include a ride around much of the Isle of Wight and a stay with a friend on the island. We also rode the Kennett and Avon Canal from Bristol to Reading
We found that the Sustrans recommend routes where the best possible choice for getting from one location to another. The routes are well planned and are the most efficient way for cyclists to get from one location to another. Some sections of the routes can be very difficult and are on moderately busy roads while other sections can be very pleasant if on a dedicated cycleway.
Most the cycle route surfaces are ridable using road bikes with wide tires, we use 32mm tires but we were wishing for mountain bikes in many areas. In general, road surfaces in England are very rough and trails and paths are not maintained. In southern England many of the surfaces are covered with sharp pieces of chert since this is the most common type of stone in the area. We use Continental Gator Hardshell tires and have never had problems with flat tires.
A section of bike path along the Kennett and Avon Canal. Many sections of bike routes not on main roads are overgrown with vegetation, not just along canal towpaths
- Travel Tips
The UK operates a system of privatized railroads, each providing service to different areas of the UK. This has created a maze of rules to follow for the cyclist trying to take their bikes with them on the train. We were able to travel with our bikes regardless of the what the ticket rules said about having to register the bike to secure a space on the train. In many cases the ticketing app said we must reserve a space but there was no option to do so, and without any other choice, we brought our bikes anyway. The conductors never asked to see any bicycle reservation. So bottom line, just don't try to take your bicycles on trains during rush hours or in busy areas such as central London. If you follow this advice, you won't need a bicycle reservation and there should be plenty of space on the train for bicycles.
- Elevation Change
The Uk is reletively flat but has many rolling hills on most of the bike routes. Its nothing like the Swiss or French Alps but nothing is really flat unless you are following a canal path.
Yes, the UK has hedgerows but on roads that are designated bike routes we found very little car traffic and people were driving slowly. Drivers can't see any better than bicyclist and were going slow despite what is seen on Doc Martin.
- Kennett and Avon Canal
This canal route is well worth doing along with a stay in Bath if you are in the area. Here is a detailed description from a person who has done the route WillCycle Kennet and Avon Canal cycle route.
A series of locks on the Canal. There are almost 30 locks in this area.
- Best Season
Spring and fall. Summers in Europe are increasingly hot and many hotels don't have AC. July and August can be wet, we frequently have had thunderstorms in early June although the rain didn't last long. No rain at all on this trip, mid May to mid June.
Signage was good on all sections of the routes we used.
A typical english breakfast at a hotel. The food is British but I like it anyway and I love fish and chips.