So what does Britain do if there is no German invasion of Belgium? Do they declare war on Germany anyway?
IMHO : NOT right away.
I agree with some of my ... critics, that Belgium, respectivly its invasion was not THE main reason for Briatin to go to war - it was more kind of an "icing on the cake", as it served so well a formula (of excuse ?) for not only the public opinion to present but also quite some of the cabinet members (the two, that at last resigned were also only ... a "tip of an iceberg").
The important point was the control of the channel coast - of belgian as well as fench channel ports.
But , with a Germany that declares its "desinterest" in Belgium, if only noone else "taps" it (same as the french "guarantee" given on british asking) as well as a german declaration of no-intent to attack France, only afraid of not to be stabbed in the back by it, this reason ceases.
However, Britain will still give France the "guarantee" to protect its northern coast from any german (naval) attack, maybe even the guarantee of its merchantmen ships worldwide (possible interpretation of the guarantee given OTL to Cambon on 2nd August by Grey), probably topped with the promise to "support" France (economically, financial) whereever possible - short of participating in the/a possible war.
Until somewhere around 12th August (
the date the french mobilization would have been (mostly) completed and France would most likely declare war upon Germany in fullfillment of its alliance with Russia as well as the written doen agreements about military operations - as well as Poincaré and Viviani told russian ambassador Isvolsky at night of 1st to 2nd August) Britain might still try to broker some kind of "arrangement" though without success ... IMHO.
Intersting question would IMO be, how the other participants "react" to this attempts in the meantime and how these are ... received/perceived by the brits.
Also "interesting" would be the question of how "fast" the Ireland-question continues to develop, maybe once again shifting political interests more towards Home Rule.
With the begin of hostilities Britain would most likely "demilitarize" the channnel in forbidding any other "vessels of war" to enter it - ofc beside the RN to "enforce" this rule.
A in this situation it would serve Britains assumed support for France as a for the moment neutral, they instead or even before the US would ask and recommend the belligerents to strongly respect and obey the rules of the London naval conference of 1909, though they didn't ratified them by themself.
In the further course of the next maybe two to three months at least Britain would probably try to still "limit" the armed conflict strongly recommending everybody else (Italy, Ottoman Empire, Greece, Bulgaria, Romania, Japan ... have I forgotten someone ?) to stay neutral and out of the conflict, playing the role of "preserver of the neutral rights" (
taking away this position from the US maybe ?).
From then ... it IMO becomes more and more problematic to "draw" Britain into the conflict.
- There will be wide coverage of the slaughter/"bleeding white" of the french in the battle of the frontiers, not the best "propaganda" for someone to join armed forces to take part.
- The irish question would/could be again much more present, depending its developement. But tbh : I struggle to see it be rather "peacefully" solved within the named timeframe of 2-3 months.
- There will be huge profits being made by trading with (all of) the belligerents and financing their war efforts/purchases worldwide, which could - in the eyes of the "city" (that wasn't a "fan" of the war IOTL) - only be endangered by participation now.
IMO only if the "hawks", rather Churchill alone, than in conjunction with Grey, who IMHO wasnt much of a "belligerent" and would have been happy if Germany/Austria/Russia/France would have been "contained" by diplomatic means, "produce" some form of incident or incidents deliberatly, Britain could enter the frail - preferably on the "Entente"-side.