Under certain conditions, Britain could certainly be invaded. If for whatever reason, America and Britain went to war today, you'd see Americans storming the beaches of Sussex. A millennium ago, the Normans Sealioned England. If you want to bring up Sealion, keep it to Nazi Germany ca 1942.
Yes, under conditions that last existed around 1100 AD.
The Royal Navy LOVED fighting the French Navy (save one fateful day off the Virginia Capes). The French produced great ships that made wondeful additions to the Royal Navy. The French fleet made more then one British captain a rich man.
The RN wasn't going to be defeated by a swarming tactic. Only a land commander would have even considered such a thing as remotely possible. I can see the Admirality rubbing its collective hands to gether just thinking of the prized to be had from this sort of loopy strategy.
As far as the current day - Even in the ASB event of an Anglo/American War you would not see a land invasion. I know you used it to illustrate a point, but no country with multiple SSBM carrying D5 missiles has to worry about a ground invasion. Ending civilization maybe, invasion no.