Not correct. Britain was a guarantor of the neutrality and inviolability of Belgian territory’ irrespective whether the Belgians themselves respected the Treaty of London...
This.
If Belgium sides with Germany - which is what it would be doing by letting German troops through, see Hague V 1907 art. 5 - then
both Belgium and Germany have violated the London Treaty. If a violation of the London Treaty is a casus belli for Britain in OTL, then a double violation of it also is, in this TL too.
Sure, it's harder to sell the public. Much less of a problem in 1914 than today. The poor backstabbed sods would just be the French, with the accomplicity of the sly Belgians. The poor mistreated civilians would be French, etc. The war might be less popular, still it has to be waged.
This would be done for the sound geostrategic reasons for which London signed the
London Treaty in the first place. Better to have the closest continental coasts in possession of small, neutral countries, and better to have them fragmented among several countries, than having them in possession of one, big, hegemonic continental power - obviously. The side disturbing that arrangement clearly intends to become that one big hegemonic continental power, and needs to be intervened against, as per usual century-old British policy.
Note the power trying this also has engaged in a naval escalation, challeging the Royal Navy's dominance on the oceans. So, a two out of two on the London red flag scale. It's war.