According to John Keegan in his book "The First World War", the British general staff had agreed to send troops should Germany invade Belgium, thus violating the Treaty of London of 1839. Both the French and the British had reasons to believe that Germany was going to do just that in the event of war with France.
For one, the Franco-German frontier was extremely fortified in 1914. Attacking through there would be difficult and costly for either army. Belgium, on the other hand, would be easier, at least in the eyes of Schlieffen. The tiny Belgian army was expected to collapse in the event of German attack, and since Belgium had refused to allow either French or British troops into their territory, defeating it would be presumably easy.
The British had made no formal commitments such as an alliance or a treaty, except for the Entente cordiale which didn't bound Britain to send troops in the case of war. Nevertheless, the general staffs of both countries had already decided that Britain would intervene by sending an expeditionary force to face the Germans in the Low Countries. This was contrary to what Schlieffen believed. He thought that the British would try to divide Germany by conducting an amphibious operation in their north coast.
In 1912, Foreign Secretary Sir Edward Grey expressed in a letter that "If either government, had grave reason to expect an unprovoked attack by a third Power, or something that threatened the general peace, it should immediately discuss with the other, whether both Governments should act to prevent aggression and to preserve peace, and if so what measures they should take in common. If these measures involved common action, the plans of the General Staffs would at once be taken into consideration, and the Governments should then decide what effect should be given to them."
Basically, Grey stated that if either France or Britain were to be threatened by Germany, the respective plans of both countries would be put into action, meaning Britain's expeditionary force would be send to help the French in Belgium. However, when the hour of truth came and France, Germany and Russia were within hours of declaring war on each other, Britain hesitated to actually declare its allegiance.
The cabinet debated the issue, concluding that the Treaty of 1839 would force them to intervene, but Belgian neutrality had not been violated yet. The Cabinet did mobilize the Royal Navy and it also assured France that they would protect the French northern coast, but they were not willing to go farther than that. The question was rendered moot when Germany issued an ultimatum to Belgium.
Now, knowing what Britain would have done had the Germans respected Belgium's neutrality is hard. As I already said, Britain had made no hard commitments and it wasn't until Belgium was actually invaded that Britain finally acted. Yet, the British were suspicious of the Germans, and would most likely had sided against them eventually. There's also the fact that both the French and the British were completely sure that Germany would violate Belgium's neutrality, thus Britain's vow to intervene to protect Belgium was in practice a promise to enter the war.
I think that, based on the evidence, we can conclude that Britain would have joined the war eventually. It had already agreed to intervene if Belgium was attacked, an attack that Britain considered would take place no matter what. The British Staff and the Royal Navy had already made plans to help the French and destroy the Kaiser's Navy. Britain was not bound by any treaty, and would most likely attempt to solve the crisis diplomatically had Belgium not forced its hand. It's reasonable to suppose that the British government would have tried to reach a compromise, and when that failed it would declare war on the grounds that the Germans were warmongers who refused peace and were invading France.
Source: John Keegan, "The First World War" mainly.
I will preface this by saying that Niall Ferguson says no. I disagree with him.
The balance of power issue has been a persistent one for the entirety of post-1500 European politics. The 30YW, Spanish Succession, 7YW, Austrian Succession, Napoleonic, Crimean, Franco-Prussian, Prusso-Danish Wars were all fought to stop one country becoming dominant.
In the case of WW1, Germany had outstripped British manufacture by 1914. Not only was there a greater industrialised workforce, but the material output had increased beyond UK capacity. In particular in steel. (1) Germany had therefore become a threat; by 1914 they only amounted to half the tonnage of the British fleet, but that was reason for fear enough. The Admiralty's rule was for Britain's navy to rival the next 2 greatest fleets - Germany was jeopardising that balance. (2) Therefore, Germany was posing a threat; to maintain the balance of power Britain would have had to get involved, as the greater power.
Also, the Schlieffen Plan. The French were so prepared on their Eastern and Italian borders that there is no way that the German army could have attacked France with sufficient speed so as to avoid the two fronts problem. Had the Austrians been a little more switched on, I believe it is possible an offensive could have been launched through Italy. Entirely hypothetical though.
With all this in mind, had Germany not violated Belgian neutrality, I would argue it is a foregone conclusion that Britain would have entered. The German war machine was such that she would have thrown everything at France, in the hope of avoiding the 2 fronts, which would have required British support. When the only other juggernaut on the continent starts swinging, the British would have been forced to intervene. (3) However, there is no way von Moltke would have launched an attack without the Schlieffen Plan. So the violation of Belgian neutrality was inevitable.
Hope that answers your question!
1: https://warwick.ac.uk/fac/soc/economics/staff/sbroadberry/wp/geruk1907bm7.pdf
2: Ferguson, The Pity of War, 85.
3: Hastings, Catastrophe, 5-10.
Edit: Formatting