The timings are important to remember in our age of shit going viral on the Internet in hours. In 1914 phones were not common or reliable and governments relied on telegrams which by their nature are slow and require the use of expert operators. 6 hours to get a message from the British government to the recon units of the German army might well be physically impossible in the conditions of 1914.
The timings are important and they factor in for my opinion that the British government reacted to the information that Germany was intentioned to violate Belgium, and not to the information that Belgium decided to resist that.
That said, I think I did not explain myself thoroughly enough. The countdown (of 5, not 6 hours, I checked: the meeting took place at 7 pm) was not starting from the British government: the meeting was between the British ambassador in Berlin and the German Foreign Minister, so it started once the
German government was apprised of the midnight deadline. Additionally, the British did not demand that, by that deadline, the German vanguards actually began withdrawing from Belgium; they only demanded that the German government issued a note of their intention to do so.
Of course this would still have required gathering the German ministers, the Kaiser, and, I guess, a bunch of generals. Then it would have required convincing the actual decision-makers from among the group to give up on everything: the Belgian invasion, their war plans, their mobilization, the golden opportunity (they believed it to be such), in sum, the whole war. And with it their credibility and future careers.
For some reason, Bethmann Hollweg dined with the British ambassador instead of trying to summon his cabinet, and spoke as if Britain were already at war with Germany.