With the 100 year anniversary of World War 1 coming up, we're sure to see lots of questions like this. The thing is that the BEF made up a very small fraction of soldiers deployed to defend France during the initial invasion in August 1914. After the battles of the frontiers, which France lost, the full on retreat of the French forces seemed to indicate that France would fall quickly against Germany. The British Expeditionary Force was a small part of the overall army, but that isn't the point. War is about the margins. The BEF held the most important areas at the far right end of the German flank (the allied left flank). While the BEF retreated along with the rest of the Allies in late August, their resistance at the first Somme, along with the French regrouping, helped prevent Paris from falling.

This isn't to say the Schlieffen plan might have worked if they hadn't been there. German soldiers were largely exhausted by the relentless attack against French forces, and the march through Belgium all the way down to Paris took its toll. I would venture to say that without the BEF there would have been at least a shot at the Germans taking Paris, but it was no sure thing.

The best book by far (and one of the best histories ever written, in my opinion) is Barbara Tuchman's The Guns of August. Highly recommend it.