First, I think a bit of the original post itself is in error. Britain did ally with Japan to prevent a possible Franco-Russian naval threat in the Far East. However, in the 1905 war neither France nor Britain wanted to be involved. Indeed, I believe the treaty did require military aid if and only if one party was at war/attacked by more than one enemy. This was not the case in 1905. For both Russia and Japan.

1914-

Now, Belgium's neutrality was guaranteed by all the Great Powers of Western Europe, and was seen by some as a stabilizing factor in the balances of power (preventing a long contiguous Franco-German border). Note that one country guaranteeing this was Britain. If Belgium was invaded, then Britain had a clear casus belli.

British policy on the Continent since Elizabeth I had been to preserve a balance of power, such that no one country ever grew powerful enough on land to devote its resources to challenging Britain at sea. With the Anglo-German dreadnought scares and the Kaiser's bellicose language, tension did exist between Britain and Germany. Additionally, the Cabinet had authorized 'talks', essentially joint planning sessions with the French Armed Forces for the deployment of a 2-corps British Expeditionary Force to the continent. The talks were finalized well before the war, as was the naval division of labor with the bulk of the Marine Nationale deployed in the Mediterranean to escort XIX Corps d'Armee from Africa to Europe.

Thus, we see that the Cabinet had at least tacitly authorized planning for a continental commitment, although many ministers, and a large chunk of the Commons remained committed to peace. The German invasion of Belgium proivided the necessary casus belli to put those plans into action, and sway the majority needed for a DoW, but the plans were in place long before the war.

Not Anti-French

To elaborate on British policy - it focused on a continental balance of power so that no state grew too powerful. France, for most of the 1800s and the 1700s remained the most powerful state in continental Europe and it took a coalition of Great Powers to break France every time. This explains British wariness of France - a powerful rival, one which had from 1792-1805 dominated Europe for more than a decade, and had conflicting spheres of interest.

Now, in 1871 that all changed. Germany was a nation of more than 60m people, with a massive and fast-growing economy, and a strident claimant for colonies. It clashed with Britain(and France) over battleship building, colonies (see - Samoa, Morocco), and British industrialists repeatedly warned of German (also tbh American) competition. The maintenance of the balance of power now involved chaining Germany rather than France.

Now, as to whether Britain would have declared war? Yes. The planning was already in place and the Empire could not risk a continent dominated by any single power, as we have seen for a very long time. It may have delayed the British, though, perhaps until the Germans were through Belgium. The British Army would not be in time for Mons or the Marine, and the French flank weakened. Alexander von Kluck would certainly have come far closer to Paris, but one must remember that France would still have fought past losing Paris. It did in 1871, and now the will was stronger. England would be in time to fight the war.

Sources - 1) Barbara Tuchman The Guns of August 2) Christopher Clark The Sleepwalkers 3) Paul Kennedy The Rise and Fall of British Naval Mastery