In 1914 there wasn't the 'machinery' in place for alternative courses of action, it took the experience of WW1 to show that the link between politics and military action was poor. As it was Britain did take an alternative course of action; they delayed their DoW for several days and then limited their contribution to 2/3 of what they planned.
I concede that mindset of the day tended to push black-and-white approaches on decisions on this level, but in a sense, Britain had *already* carried out more limited alternatives over the previous days: Churchill's decision to keep the fleet mobilized, and the promise made (privately) to Paris that Britain would not allow the HSF to come down the Channel each constituted "measures short of war."
But beyond that, I do confess that an invasion of Belgium was going to create more pressure to go to war than to resist it, even for a Liberal government; I can understand how they got there, even while thinking it was a very grave mistake (even, to some real degree, in foresight, as Ramsay MacDonald recognized). It would be more instructive, I think, to see what a scenario that did *not* involve an invasion of Belgium - the Germans go east, or even get Belgium's permission to march through (as Geon's timeline proposed) - might have impelled in Westminster. But I recognize that this is not what the OP is asking here.