Since no one has answered this question, I will try and take a stab at it.

Someone far better qualified than me, has already written very good answers on why the British didn't conduct a naval invasion of German held territories: https://www.reddit.com/r/AskHistorians/comments/45l3ap/was_landing_soldiers_behind_enemy_trench_lines/czywz8v/ by /u/thefourthmaninaboat

I'm by no means an expert on the Royal Navy during WW1 and their strategic thinking, so I will only give you a few examples on why an invasion trough Denmark was not a very good idea.

1. Denmark was neutral during WW1 and the British reason for joining the war, was the German violation of Belgian neutrality during the German invasion of France. The British utilized the "rape of Belgium" to a large extent in their propaganda, so it would not look good for them if they did the exact same thing to Denmark.
2. The Germans were anticipating this move. already back in 1906, the British promised the French that they would launch and invasion trough Esbjerg in Jutland with 100.000 men in case of a war between Germany and France. This promise was soon revealed to the public and the Germans took account of it in their future planning. The Germans conducted numerous military exercises in the area to prepare for an invasion and in 1916, they started constructing a formidable defensive line across the Southern part of the Jutland peninsula in what was then part of the German Empire, the so called Sicherungsstellung Nord. This was a state of the art defensive line, with concrete bunkers, heavy artillery, trenches, barbed wire etc. it was built based on all the experience available from the trench fighting on the Western front. Contrary to the trenches on the western front, the Sicherungsstellung Nord was very optimal, since the Germans didn't have to construct it in an active war zone. You can read more about it here http://www.military-history-denmark.dk/Sik_nord_GB/index.htm