Barbara Tuchman mentioned the something similar in The Guns of August. In fact, she claimed it was highly uncertain Britain would go to war at all if the Germans avoided Belgium as well. The Germans were trying to provoke the French to cross into Belgium first, but quickly ran out of patience (especially given that they were under a lot of time pressure to finish the war on time) and invaded it first. Tuchman considered this to be one of Germany's biggest mistakes of the war.

From a purely military matter, a belgian neutrality violation would have made sense. Joffre certainly pushed for it with all his might.

On the other hand the british warned the French against doing so. Even worse, the belgians were very jealous of their neutrality, and the french politicians assumed they would throw their lot with the germans against them.

Given that a very significant reason for the germans failure in 1914 was the belgian resistence in the forts , and later in the yser, having the belgian army on its side would have mean - in my opinion- the defeat of France in 1914.

Despite the attractiveness of Joffre’s appeal, Poincaré—like Caillaux before him—refused to let French forces enter Belgium before a German violation of neutrality. The premier insisted that Belgium would never agree to France’s violating its neutrality and that a violation would probably result in its joining Germany. More important, a violation of Belgium’s neutrality could cause Britain not to support France.

Pyrrhic Victory: French Strategy and Operations in the Great War - Doughty

After the Treaty of Vienna and the partitioning of Europe post-Napoleon, the creation of the BeNeLux states had to be protected somehow. They were sandwiched between France and Prussia (later to become Germany), and if European politics progressed like it had, these mini states would be gobbled up sooner or later by their much grander neighbors. For this reason, Britain pledged to safeguard Belgium neutrality.

Indeed, this was their greatest treaty obligation before the war. While the French pushed hard for them to join an alliance in the early years of the 20th Century, Britain only made cautious responses to them, never pledging their aid to France against Germany, unless an invasion of Belgium required it. Should France have invaded Belgium, it's quite conceivable that Britain would have aided Germany against France.