Within England, the answer is The Cycle Streets site which will generate much more accurate and helpful cycling routes than Google, and could certainly be used to get you from London to the coast. It also generates astonishingly traffic-free routes through London itself.
Outside England, I can only suggest using the Open Cycle Map, which covers most of Europe. I don't know with what accuracy, but would tend to trust it at least in France, Germany, and Benelux, where there are strong cycling traditions. It shows the main national cycle routes in red, and local ones in blue. The Dutch network is very clearly signposted. You can use it with ViewRanger on a smartphone, though you'll need a data connection most of the time (it is possible to cache particular areas in advance)
Viewranger and RidewithGPS do bicycle route planning but neither, in my experience, are as good as the cyclestreets site. Sorry. I don't have the reputation points to post links to either of those two programs. Google is your friend.
There is also an established "route verte" from London to Paris, but I know nothing aobut it except the name and that it exists.