Facing a German hegemony on the continent would be something the British wanted to avoid at all costs.
Well, in this case, they did avoid it at "all costs." Because defeating German continental hegemony (or what they perceived to be such) cost them over a million dead (the utter gutting of an entire generation of British men, especially when you add in the 1.7 million wounded, many crippled for life), and their financial, maritime, and naval supremacy for all time - and, before long, the empire, too.
But given the obvious divisions within Asquith's cabinet, it's clear that not all British decision-makers in 1914 perceived
hegemony to be at stake, or if they did, that defeating it would be worth the cost in blood and treasure. Edward Grey's views were not universally shared in London, even if they did happen to prevail in August 1914.
I do think Ferguson is right to ask: Was it really worth the price Britain paid?
EDIT: The Irish question had been brewing for a long, long time, but the British handling of the 1916 Easter Uprising was the last straw. What should have been a simple "march in and round up the insurgents" act through clever peacekeeping forces deployment and careful police work was instead handled by artillery, one of the most inaccurate ways to suppress a revolt and one that caused a massive amount of collateral damage. The subsequent actions carried out by the troops, embittered and made cruel by two years in the trenches, exacerbated the issue, causing many Irish to have legitimate grievances against the British.
With a gentler and more careful hand, we could have seen a Home Rule system in Ireland. Instead we got the jump up into a full-on independence movement.
I don't necessarily disagree. But I do think that the pressure and distraction of the war contributed to the harshness of the response.
If Britain is not in the war, it cannot just table the question of home rule which was coming to a head (via the Government of Ireland Act 1914) in 1914.
While Britain and Japan could be nominally neutral, the Japanese were expanding, hungry, and eager for their little slice of colonialism. They'd find an excuse to start grabbing someone's stuff in the Far East if they thought they could get away with it.
I don't disagree with the basic characterization. But Britain's entry into the war gave the Japanese not only the excuse they needed to enter the war (via the alliance treaty) to grab German spoils, but also the assurance that Germany would have zero chance to interfere given that they would be blockaded by the Royal Navy, to say nothing of the greater assurance that German victory was now less likely, or at worst likely to be enormously costly and long in coming.
It seems evident based on what we know of Japanese cabinet sentiment that they would have been forced to sit back, watch and wait for a while - and the war might be over before they could find an opportunity to go to war with Germany on their own hook.
More likely, Tokyo takes the opportunity instead to expand their position in Manchuria and China.