Just to be clear the Eastern Front refers to the Russian Front of the war, the British and French were engaged on the Western Front. The Royal Navy, while powerful, did not control the Baltic Sea. A naval invasion force from England into the Baltic Sea ,would have to defeat the German naval forces in both the German Bight and the Baltic, as well as along the Danish Straits. No element of surprise could be maintained, and the Germans could readily muster land forces to meet the landings. The force would be impossible to supply, as this route could easily be controlled by the German navy, especially the U-boat force. A landing on Baltic side of the northern coast of Germany would have little direct influence on the strategic situation on the Western front where the British were fighting, and would therefore garner little support from the civilian leaders in Britain, especially after the failed Gallipoli campaign. The Germans would see this as a chance to defeat the Allies in a decisive naval battle, as the Royal Navy would have to commit significant resources to protect the invasion force.

Broadly the Belgian coastal areas were known to the Allies as the German 'Naval Flank', and as the land war had become static, great interest was paid to it. The stalemate had created an interest in indirect approaches to winning the war. The British had considered an amphibious operation on the Belgian coast several times, including one known as Operation Hush, which was set occur after the 3rd Battle of Ypres in 1917. The operation was ambitious and included landing tanks on the beaches east of Ostend, behind the German lines. The 3rd Battle of Ypres was to capture the railway line that supplied the German front, and combined with the landings, the Germans position in Flanders would be untenable. The 3rd Battle of Ypres did not take the Railways as expected and the operation was called off. Other operations of note were the Zeebrugge and Ostend raids, both examples of the indirect approach.

Remaining on the defensive for the whole war was not really a solution. The war was incredibly expensive to maintain, even when not attacking. The cost in men and materiel just holding the line, was extraordinary. The Germans in 1917 had switched to Unrestricted Submarine Warfare, which not only sunk ships supplying the war effort to Britain, but began to deter some shipping from occurring at all. If the Germans were not kept in an attritional battle, and allowed to build their strength, the risk of the Germans gaining the initiative grew. By waiting them out, essentially you would be playing into the hands of the German Abwehrschlachten, or defensive battle, in which gaining time is critical. By not trying to solve the deadlock and gain the initiative, there may be a chance that the Allies would lose the war. The Germans would also still be looking for a Decisive Victory, and would continue attacking. Had the Germans been allowed to build their strength over time, there may have been the conditions for a campaign like Operation Michael to be successful, however unlikely that may seem. The morale and fighting spirit of the allied armies would have been affected by remaining in a defensive role, which may have caused unrest and instability and perhaps weakening their defensive capacity.

The blockade of Germany by the Royal Navy was working, but was not capable of stopping all shipping around Germany. The German effective use of the U-boat meant that the British maintained a distant blockade rather than a close blockade, which offset its effectiveness somewhat, as did stockpiling and other measures within Germany. Politically, allowing Germany to hold the land it had gained without consequence, as well as to continuing to conduct operations against allied shipping is also not an option, as the morale of the population and fighting forces would be affected, as would the credibility of the Government in power.

EDIT: I have just discovered that Churchill was considering an operation to invade Germany from the Baltic.. It was apparently rejected due to reasons similar to the ones I mentioned. This lead to the Gallipoli campaign instead.

Sources: The Naval Blockade. by David T Cunningham

An Examination of the 1917-1918 U-Boat Campaign in Light of B.H. Liddell Hart's Theories of Indirect Approach. by CDR C.S. Hamilton.

Operational Art in the Defense: The German “Abwehrschlachten” in 1918. by Major by Frank Reiser.

Navigating through torpedo attacks and enemy raiders: Merchant shipping and freight rates during World War I by Jan Tore Klovland.