The UK probably wouldn't have taken a "you made your bed" attitude while the Germans savagely beat the French halfway to death (cause let's be honest. Europe 1914 was a giant garbage fire waiting to happen. Something would have set the thing off eventually)
I mean IOTL even the UK had to just sit back after how recalcitrant France was after the assassination. I mean didn't their response to German repetition requests translate to "we recomend a better guard detail"?
So we'd end up with France and UK in the West, and the Russians in the east. The big question is if the UK can draw off enough troops from the east that the Austrians don't get bailed out.
Let things drag on for another 6 months, and Russia would basically overrun Austria-Hungary, and then Germany is screwed.
And of course the UK probably slows or stops its build program for however long it drags on for, and a fair bit of the RN and HSF sink each other. So no big 40 battleship/cruiser fleet to bludgeon the Japanese with I'm 31.
Having Kaiser Willy get plugged might have been the best thing for Germany, ironically.
Is Britain willing to try deploying the Army to the Continent during such a critical time on Ireland? Remember, the Curragh Loyalty Rally occured less than a week after the assasination, after the whole "Churchill's Sealed Envelope" scandle. The British public was thrown into shock when it was revealed the kind of military crack-down that unofficial committee of Liberals was planning on imposing on the Ulstermen to enforce Home Rule, especially once the "Hoolagins" of the Irish Volunteers started their own pogroms after reading and exaggerating the unproven allegations of the Ulster Volunteer's conspiracy to seize British garrisons the Envelope Plotters were using to justify their actions. Without the critical presence of armed British troops under officers fully dedicated to the cause and with the trust of their troops to prevent the violent clashes between the radicals among the Nationalists and Loyalist factions from spiraling out of control during the Parliamentary Elections and the Balfour government's delicate negotiations, you run the very real risk of compromise getting eluded and civil war/disorder breaking out in your rear just when your army is tied down on the Continent.
Even then, where exactly would the British squeeze their troops? The French army was packed to the bursting on the Franco-German border at the start of the war: it's part of what contributed to their being so disorganized and short on ammunition during the campaign. Too excited to show their
elan and bayonets to remember to leave room in the train cars for artillery shells, replacement gear, and all the other "sinews of war" which we'd all quickly learn would have been vital to getting combat-ready again after their early loses. Instead, units just kind of... wore down as the Germans chased them down. I suppose the arrival of fresh British divisions, if they had their own dedicated logistics system under British management, could "stopgap" the German counter-attack and give the Frenchies time to resupply, reposition, and regroup for a more extended campaign if you had enough of them. But diden't London's warplans only have 6 divisions earmarked for expeditionary force at the time?
Money would definatively be re-routed from the Royal Navy to the Army, though, so you're definatively right on the build program.
Having Wilhelm the III in charge in the 1930s caused a bit of a scandal though. He was an infamous womanizer. How would that play out if his father was still alive?
To be honest, I think Wilhelm II would be secretly proud of his son no matter what the public reaction was. Wasen't the man a little obsessed with being "Manly"?