Britain did not solely declare war on Germany because of Belgium. They had been wanting an excuse to fight Germany for a while, Belgium was just the justification they used.
I hate this theory. It is principally put about by apologists of the Central Powers who ignore the internal political situation in Britain at the time and wish to minimise the absolute German war guilt for British entry. (I am not saying that is the case with yourself)
The Government nearly fell over the declaration of war in OTL. As it stood, four Cabinet members resigned over the declaration alongside a Junior minister. David Lloyd-George came within an ace of resigning himself over the declaration. Without the invasion of Belgium, there is a strong possibility that he would have gone forcing a leadership crisis in the country with the government possibly collapsing.
I cannot see Asquith allowing this situation to arise.
Bear in mind, even without the justifiable reason of the invasion of Belgium, the declaration of war on France was also a justifiable reason. Again, pointing to German war guilt.
As for the "excuse to fight Germany". That is just rubbish. There was a fear of Germany. Since the Battle of Trafalgar, the Royal Navy controlled the trade routes of the world, maintaining the Pax Britannica. The Germans decided it would be a good idea to challenge the supremacy of the Royal Navy, not only putting the trade routes at risk but the United Kingdom itself, forcing a naval arms race.
The risk could have been avoided if Germany maintained itself as a land power rather than acting in a way which would alarm the British government.
Leaving all this aside, the principal priority inside the UK until very late on was not in Serbia, but in Ireland. Had Germany not invaded, we could easily have seen Irish Home Rule within the UK. We could even have seen a Civil War inside the UK over Ireland. It was only postponed due to the Great War after all.
There is little doubt that Britain could have been dragged in eventually if the war lasted. I will point out though that the British were not dragged in during the war of 1870.
German aggression in Naval terms forced a reaction. German aggression in declaring war on France made things possible. German aggression in invading Belgium made it inevitable. As such, I agree likely, but far from inevitable.
Edit: And as has been mentioned, the King was not where the power lay in the UK. The Government were. The Germans would need to negotiate with the British Government, not the King. A few decades later, a King who challenged the Government found out what happens when he tried.