There were several big problems with an invasion of Britain from Scotland that made it completely impractical, especially compared to the already difficult and implausible option of invading from France.

From the German perspective, one big problem with invading from Norway was distance. The closest distance between a port in Norway and one in Scotland was about 450 km, between Stavanger and Peterhead. This compares poorly with the ~40km between Calais and Dover across the English Channel. Distance imposes a number of major problems for an amphibious assault. It greatly increases the amount of shipping needed to keep a beachhead supplied. If you are supplying a beachhead a day's sail away, and your beachhead needs one shipload of supplies per day, then you need at least two ships to supply it; one carrying supplies to the beachhead and one returning empty. If you double the distance, then you need two more ships, and so on and so forth. This was a major problem for the Germans - they barely had enough sea transport to support a large-scale landing across the Channel, having to significantly supplement it with barges from the European river and canal network and extemporised short-range solutions.

It was also a problem for the German air force. In any landing, this would have several key roles. It would have to defend the convoys and beachheads from any British air attacks. It would have to attack British naval forces, airfields and troop concentrations, making up for the weaknesses of the German navy and the lack of artillery that could be landed. The distance was a major problem here. Most German fighters based in Norway could not reach Scotland, so could not protect the beachhead until airfields ashore were captured or established. Nor could they escort bomber raids. Only the twin-engined Me 110 could reach Britain from Scotland, but there were comparatively few of these (~300 against ~800 single-engined fighters) and they were no match for Spitfires or Hurricanes. On the 15th August 1940, the German air force in Norway attempted attacks on targets in northern England. The RAF claimed 45 kills for zero losses, even against a raid escorted by Me 110s, and very little damage was done. This was the last attempted daylight raid from the Norwegian bases. Without air support, the landing was impossible, and based on this experience it was unlikely at best.

Another huge problem was the British Home Fleet. It had a major base at Scapa Flow, very close to the sea lanes between Norway and Scotland. It greatly outnumbered the German Navy. On the 1st July 1940, the German Navy's heavy units consisted of two capital ships plus two large cruisers, a heavy cruiser and four light cruisers. Many of these ships were out of action for repairs. Both capital ships had been torpedoed off Norway (Scharnhorst by the destroyer Acasta and Gneisenau by the submarine Clyde) and would not return to full readiness until autumn weather had made a naval invasion too hard. Of the large cruisers, Scheer was in refit until October and Lutzow had suffered heavy damage in the Norwegian campaign. Only the heavy cruiser Admiral Hipper and the light cruiser Koeln were ready for action in the summer of 1940. At this time, the RN had four battleships and three cruisers at Scapa Flow, plus two more cruisers at Rosyth, three more at the Humber and an AA cruiser at Newcastle. All of these ships could easily respond to any attempted naval invasion of Scotland's east coast; given the paucity of the German escort, it would easily be crushed. In later years, the British did lose ships or transfer them to other theatres like the Mediterranean, and the Germans did repair or commission new ships. Even so, the balance of power in the North Sea was still heavily in British favour.