This is an interesting question which really went through the British mind in two phases during the war.

The first phase during which was considered was in 1914. The rout of the Allied armies and the driving of these forces back to the Marne were not even remotely considered by major authorities in French or British governments. For the French, it was always Plan XVII, by Joffre, which occupied the military train of thought - the French would send forces into Belgium, if need be and war was declared on their northern neighbour, while undertaking a grand offensive into the lusted provinces of Alsace-Lorraine. For the French, naturally, it would always be about holding the homeland. They would sacrifice anything to hold the Germans before getting to Paris, akin to the 1870 war.

For the British, this was also important. They need to get their 250 00 strong army, the British Expedtionary Force, over to France and partake in operations as quickly as possible. This was designed in pre-war secretive military meetings between Sir Henry Wilson, as Director of Military Operations, and the French General Staff, as well as in the opinion of pre-war C.I.G.S. Sir John French. Facing the exact same problems as the Allies in WW2, they also need to supply these massive forces to be militarily effective (Mind you, this all in mind of having just an elite, small B.E.F. in France, not the monstrous Kitchener's New Army!) while also committing to the defence of their tiny ally and linchpin of the entire front - Belgium.

Hence, the Channel Ports become paramount in importance beyond perhaps even Paris. These is shown, as a bit of trivial information, in two war offensives. One; the consideration by Douglas Haig in 1918 of retreating back on Calais/Dunkirk instead of holding the Western line - i.e. breaking away from Petain's French grand army. Secondly; by the legendary German 'Race to the Sea' of 1914, when the Allied rout meant a heedless sprint for the vital Channel ports.

These ports were the lifeline of sustaining British support in WWI, so the furtherest north this was considered was at Antwerp in 1914. Winston Churchill, then First Lord of the Admiralty, proposed a general landing at Antwerp to hold the Belgian defence and keep the north Belgian front open. In the end, while some Royal Marines were sent, and perished, this was not realistic in the eyes of the War Cabinet. The B.E.F. was reeling from devastating defeat at Mons, and the Germans were pushing in on the revered Channel ports while threatening Paris itself. Any manpower, already desperately short due to a tiny British army and reserve force of only 800 000 untrained boys and unmobilized, was devoted to keeping the B.E.F. from total disintegration.

This was a theme upheld even when the front did stabilize. It wasn't until 1916 that the British were equal to the grand citizen armies of Germany and France, when Kitchener's famed 'New Army' kicked in, and millions of young men entered the Western Front. But these reinforcements, since mid-1915, had always been earmarked for use by Haig in the great 28 division Somme offensive. So, as you suggest, the priority was always strategically focussed on breaking through the trenchline. This New Army was chewed up in July 1916, and capability to conduct maritime invasions dried up.

So basically - leading generals, circumstances and lack of manpower mandated that the British could never reasonably aim at opening another front in north Belgium.

The only other seaborne invasion pre-1916 was, of course, Gallipoli. But this was an effort mostly bolstered by Dominion troops and spare British/French divisions. In the end, this experiment was also abandoned due to manpower woes on the Western Front (e.g. the Australian troops ended up heading the July Somme offensive).

This leads us directly to the second phase of seaborne consideration; the Lloyd George stage. It is well known that Lloyd George generally depised Doulgas Haig, and despite strong efforts to dislodge the Field Marshall after the disastrous Passchendale battle in 1917, royal connections ultimately maintained the general in his position. And Douglas Haig had always, always believed that the war had to be won in France - hence his stubborn efforts to breakthrough in July 1916 and September 1917.

So the Prime Minister, not having the ability to interfere tactically, and not wanting to bow down to Haig, withheld millions of British reinforcements in Britain. So here was another two marks against the possibility of Belgian landings - the manpower did not exist, as in 1916, to land troops plus keep the British armies in France alive - and Lloyd George greatly disapproved of giving even more influence to an already power-hungry Haig. In fact, his position on this did not change until 1918, during the Spring Offensive when the Germans finally broke through. But, as in 1914, it was the threat against the Channel ports which gained priority over British thinking minds rather then a adventurous, Gallipoli-like expedition towards Antwerp.

There are two extra things here which need to be added in the general war which also negated this. Firstly; Gallipoli had been a disaster. It had cost politicians their careers (Mainly Churchill) and had got the Allies nowhere fast.

Secondly; Lloyd George was in favour of 'knocking out' Germany's supports. He was in the same mind as Churchill here in that he belied by taking away Germany's supports, it too would collapse. So, while the PM was not against seaborne invasions - he was simply against Douglas Haig, and hence his unwillingless to allow the field marshall to expand further into Belgium. This is supported by his strong support for expeditions into Salonika and Italy.

So, to answer your question: lack of manpower, leadership tension and Western Front priority (In Channel ports, Somme/Passchendale offensives and the Spring Offensive). I believe small scale landings were made north of the small Belgian army at the northern-most end of the Western Front, but were of little consequence for their efforts. Anything on the scale of Gallipoli or Salonika was justly impossible.

[I forgot to state my two main sources; Charles Bean's war history (frankly indisputable in referencing) and Max Hasting's Catastrophe.]

Operation Hush, a divisional-strength landing supported by artillery and tanks was seriously planned to tie in with Third Ypres, actually progressed to the stage where the landing craft were built and the landing force's equipment placed aboard. It was cancelled because the land offensive didn't achieve the objectives required for the two forces to link up. However, this wasn't so much a 'second front' as an amphibious flanking manoeuvre.

The very first British attack proposed after the onset of trench warfare, in January 1915, was a thrust up the Belgian coast to capture a stretch of the coastline between Ostend and Zeebrugge known as the Zeebrugge Plan. While not a strictly amphibious operation this presumably would have received a good deal of support from the Royal Navy. Its aims were naval too--to deprive the Germans of their closest ports to Britain and increase the country's security, since there was at the time an 'invasion scare' (though this had little basis in reality). The reason this operation was planned as a breakthrough, rather than an amphibious flanking manoeuvre, is for logistical reasons. It was far from certain that it was possible to land enough troops quickly enough to have a chance of victory. The British (like everybody else) had very little experience in such operations. Gallipoli shows what also might have gone wrong with a landing behind German lines. Even in 1944, with the benefit of several years of amphibious warfare experience, a host of specialised landing craft, armour and other equipment, and extensive intelligence and deception efforts, the Allies were far from certain that the Normandy Landings would succeed. The British in WWI might not have had an Atlantic Wall to contend with, but everything else was against an amphibious landing being successful. On the other hand, Sir John French and most of his subordinates did believe that the western front could be breached. In their defence, they hadn't yet tried and failed, and their first attempt, at Neuve Chapelle in March, was a resounding tactical success which fell down only because it wasn't possible to send reinforcements into the gap which had been blasted in the German line quickly enough. Back in January, the government in London had been far more sceptical about the possibility of breakthough. This was exacerbated by pessimistic reports sent back to Kitchener, the Secretary of State for War, by Lieutenant-General Sir Henry Rawlinson, one of the corps commanders at the front. The death blow for the Zeebrugge Plan was actually dealt by the French, when their war minister Alexandre Millerande mentioned to Kitchener that Joffre--French C-in-C and therefore commander of the majority of Entente troops on the western front--did not think the plan was practical. Amphibious efforts were shifted to Gallipoli.

Landings were always an option, but the time was never right. It was certainly thought that landings might follow-up a breakthough, rather than being the main operation to precipitate a German collapse and allow a breakthrough. So to some extent, the generals were hell-bent on breaking the trench lines, but this isn't a case of being blind to other possibilities; it's a case of taking a straightforward land battle, of a type which was fairly well understood, over an amphibious operation which would have been a risky and possibly catastrophic stab in the dark.

During the planning for Gallipoli there was a rival scheme being put forward for a British landing in Schleswig-Holstein, the aim being to cut off the Kiel Canal, threaten the German naval base at Wilhelmshaven, divert German reinforcements from the Western Front and possibly put pressure on Denmark to adopt a more pro-Allied approach. Ultimately this idea was passed over in favour of Gallipoli but it did have support amongst those opposed to Churchill's scheme. Unfortunately I don't know as much about it as I should do, so don't have any specific sources but I'm sure someone more knowledgeable than myself on this specific subject will be able to expand upon this.

I'm hesitant to jump in here because WWI is outside my specialty, but I feel as though I should mention there's a clear reason to avoid an amphibious assault that hasn't been addressed in these replies. That would be the existence of the German High Seas Fleet. It was numerically less strong than the British Grand Fleet, but ships of the High Seas Fleet made the North Sea into debated ground at best throughout the war. To attempt an amphibious landing without total control of the landing area across the North Sea, and/or before destroying or rendering useless a large part of the High Seas Fleet, would essentially be mass suicide.

I also feel I should point out that the Germans had mined substantial parts of the North Sea and the coasts of Belgium and the Netherlands, so any amphibious attack would have to be preceded with a substantial minesweeping and local patrolling force, which would tip the German high command off to its planning and intended landing area. (Also, I remember reading in Massie's Castles of Steel that the British minesweepers at Gallipoli were essentially repurposed fishing trawlers; I don't know if that was a feature of the advanced nature of that assault or if the British did not have dedicated minesweeping vessels.)

No. For some very simple reasons: the Belgian coast is barely 60km wide and part of it was still under Belgian control after they opened the floodgates at Nieuwpoort. That leaves a very small and easily defended area to land in and it would be right next to the German frontlines. It would never work as a second front.

It also wasn't possible to try and take Antwerp over sea and the Scheldt river as that would violate the neutrality of the Netherlands and create a whole new mess.