The Germans did have a plan for an invasion of mainland Britain in WWII. Known as Operation Sea Lion, planning began in June 1940, but it was cancelled in October of the same year. I've written about it before multiple times - see here, here, and here, as well as this description of British defensive preparations. Sea Lion was essentially an impossible operation, as the Royal Navy greatly outnumbered its German counterpart, and the German Luftwaffe could not effectively suppress it. This meant that the Kriegsmarine could not win naval supremacy, as needed for an amphibious landing.

Comparing Sea Lion to Overlord shows how difficult it would be for the Germans. Planning for Overlord began in 1942, giving two years of planning. The Germans had little more than two months. The Allies had six prior amphibious landings to learn from (Jubilee, Torch, Husky, Baytown, Avalanche and Shingle), as well as more in the Pacific theatre. The Germans had no amphibious experience to speak of. The Allies had access to a plethora of intelligence source - the French resistance, special forces teams, signals intercepts, pre-war spying and so on. The Germans had no effective spies in Britain. For Overlord, the Allies had secured naval and air supremacy. For Sea Lion, the Germans had no chance to gain naval superiority, and failed to gain air superiority. The Allies brought over 1,200 warships, 4,000 specialist landing craft, and 1500 auxiliaries and transports to Normandy. The Germans had just 44 surface warships (including those in long-term repair), and a few hundred converted river barges.