As the King, I'd strongly suggest(*) to my government that they make Britain's position clear and explicit to the other governments involved, especially Germany:
- Britain's security guarantee for Belgium is absolute. Any attack on Belgium is a declaration of war on Britain.
- Britain regards the Entente as creating a moral obligation to support France against foreign aggression.
IOTL, Britain was extremely vague about these points, which the German government interpreted as an indication that Britain did not intent to actually fight unless directly threatened: the Entente was not a formal binding military alliance (there was a formal alliance between France and Russia, but not between Britain and either country), and the 1839 Treaty of London guaranteeing Belgian neutrality was not taken seriously by Germany. It's likely Germany would have been at least a bit more restrained in escalating the situation had they understood Britain was actually willing to go to war.
In hindsight (although nearly ASB without hindsight), it also might have been beneficial to intentionally leak British naval warplans to Germany. German plans assumed Britain would maintain a close blockade, patrolling the Grand Fleet just off the German coast to keep the High Seas Fleet bottled up in port, which would expose them to minefields, submarine attacks, and torpedo boat raids to whittle down the GF until the HSF had numerical parity or better. But Britain had abandoned plans for a close blockade some time before, foreseeing the obvious German response, and instead planned a distant blockade (using destroyers to intercept merchant ships in the Channel and the North Sea and keeping the main force of the GF in port ready to intercept the HSF if they sallied in enough strength to threaten the blockade patrols or raid the British coast).
Another think Britain might have been able to do would be to sponsor a formal conference, at least between Germany, Austria, and Russia. Even if Austria remained dead set on full acceptance of their ultimatum to Serbia, Russia's interests in Serbia weren't entirely irreconcilable with Austrian aims. I seem to recall reading that Russia was willing to accept temporary Austrian occupation of Serbia in order to compel full acceptance of the terms of the ultimatum, provided the occupation would be strictly temporary and Serbia would remain independent afterwards. I also seem to recall reading a claim that Austria and Russia had been close to a deal to this effect when Germany panicked over the Russian mobilization orders and declared war. If these claims (or even just the former) were accurate, then a formal peace conference might be able to improve lines of communication enough to get a deal done.
(*) My actual political power is even more limited than the Kaiser: he has broad powers to fire and replace his Chancellor and cabinet ministers, whereas I'm bound by tradition (and Parliament's willingness to use the power of the purse to enforce the traditional rules) to only appoint ministers in accordance with the wishes of the dominant party/coalition in Parliament.