I wouldn't be surprised if this one had been done before, with with an excellent ongoing thread on the Germans doing and East First strategy in 1914, I think what exactly Britain does in that event should get its own thread.
So what does Britain do if there is no German invasion of Belgium? Do they declare war on Germany anyway?
Some relevant points of consideration are the ongoing Irish crisis, the fact that two cabinet ministers resigned over the decision to go to war OTL even with the invasion of Belguim, and the fact that Britain had a minority Liberal government whose re-election prospects were not good. A new election would have had to have been held by January 1916 at the latest. Of course the Liberal leadership could have formed a coalition with the Tories, which happened OTL in mid 1915 anyway.
Also if the British stay out of the war do they deliver the two battleships to Turkey?