...or would they? They certainly did in 1941. Not that that proves anything. It's a counterfactual anyway, so all we're running on is educated guesses and personal opinions.
I agree with all of these "The war wouldn't happen in the first place" posts. So, here's a different question. What if Germany never invaded Belgium? Would Britain then get itself involved? After all, they were pretty much the only major European power that supported a unified Germany. Less troops means a smaller chance for France to fight them into a stalemate, and therefore could see a repeat of 1870.
Firstly, the Germans went into Belgium because the French were going to go into Belgium, and the Germans needed a flank guard. The so-called "Schlieffen plan" is nonsense - a political memo designed to get the Reichstag to vote for an increase in the size of the German army, and not reflective of actual war policy whatsoever, under either Schlieffen or the younger Moltke. So if you want to get the Germans to stay out of Belgium, you shall have to totally alter French deployments as well. Remember, the French issued mobilization orders sending elements of the Fifth Army to the
Belgian border before Germany even mobilized, let alone declared war on either Belgium or France. The advantage of using neutral Belgium to overlap the German flanks and their fortress system in Alsace-Lorraine was deemed too important to lose by Joffre and the rest of GQG.
Secondly, the British would go into war on France's side even if the French violated Belgian neutrality first, not the Germans. Ed Grey had that asinine idea of the "balance of power", where the British were supposed to prevent any one European country from getting "strong enough to challenge them" - whatever either of those things meant. The British had conceived of Germany as the greater danger, so no matter whether Germany violated Belgian neutrality or not, they were committed to aiding the French. The British Army had conducted - in direct contravention of Asquith's orders - staff talks with the French military for nearly a decade, on the premise that the UK and France would be fighting together against Germany. The only real block to this was political: many Liberal politicians did not want to get involved in a continental war in August 1914. However, for military purposes this was irrelevant, because Andrew Bonar Law, sniffing an opportunity to do precisely what the Home Rule Crisis was designed to do - put him, and the rest of the Tories, in power - was willing to form a coalition with Asquith for the purposes of pushing the war through the Commons. So Britain was going in any way you sliced it.