Of the members of the Triple Entente, Britain was regarded to be most reluctant to go to war, but why was this?

It has a lot to do with the fact that the "Triple Entente" really didn't exist outside the imagination of Kaiser Wilhelm and his advisors. There was no concrete alliance tying Britain, Russia and France together as a group; what there was the Dual Entente between Russia and France, and then separate 'arrangements' with Britain and each of the other powers. Neither 'arrangement', the 1907 Anglo-Russian Agreement or the 1904 'Entente Cordiale' with France and Britain, tied Britain to a concrete, military commitment. If they wanted to, they could abstain from entering a conflict if either or both Entente powers were attacked by the Triple Alliance.

With this in mind, British reluctance was tied to domestic troubles at home, notably looming labour unrest and the threat of civil war in Ireland. More importantly, when the July Crisis really developed in late July, 1914, it was still very much confined to Eastern Europe. It was only when the Germans declared war on France and Russia, and then began their invasion of France, Belgium and Luxembourg, that the threat went from being a conflict in eastern Europe to a conflict straddling much of the continent, with severe implications for the balance which the British foreign office had sought to construct. The invasion of Belgium in particular seemed to underline the threat of Germany's actions, what might be referred to in IR theory as those of a 'revisionist state', and is what led to British intervention.

Thus, British reluctance could be said to stem from the fact that it was not strictly obligated to intervene, and that the Crisis initially looked as if it might be confined to eastern Europe, or potentially resolved peacefully though Edward Grey's efforts on that front came to nought.