What was the significance of the BEF moving into the gap between German forces in First Battle of the Marne?

Question

The German troops fighting in the Battle of the Marne were exhausted and their commanders seemed to communicate very little. After the Marne they retreated to the river Aisne and more or less began four years of digging trenches. But there was one significant move by the BEF that seems to have been the true catalyst for this retreat.

On 9 September Bülow learned that the British Expeditionary Force (BEF) was advancing into the gap between his 2nd Army and Kluck. He ordered a retreat, obliging Kluck to do the same. The counterattack of the French 5th and 6th Armies and the BEF developed into the First Battle of the Marne. BBC

It was the report of their columns advancing into the gap which led Bülow to order the retreat of his Second Army on September 9. The temporary advantage which the German First Army had gained over Maunoury was thereby nullified, and it fell back the same day. Brittanica

The wording here seems to imply that the slow, cautious advance by the BEF was what set off the full retreat to the river Aisne. It might have been the final nail in the Schlieffen plan’s coffin. But surely, Bülow saw many other problems that factored into his decision. Was anyone considering a retreat regardless of the BEF? What is the actual significance of this event to the war’s outcome?

Answer 1

The British Expeditionary Force (BEF) was the "straw that broke the camel's back." Together with the French, they had 191 battalions at the critical point of the fighting versus 128 for the Germans, with the BEF providing most of the difference. In the main drive, the Germans were able to contain the French 6th Army to the east, while the BEF on the west advanced slowly but surely.

Even before the British counterattack, the Germans had been "stalled" on the Marne. But that is not the same as a retreat, which was not planned (except for local re-groupings). Although it was a relatively shallow drive, something like 40 miles, it did push the Germans away from Paris.

The first Battle of the Marne did not win the war for the Allies. But it marked the place where the Allies stopped losing it. Before, the trend had been that of "Germany winning." With Paris saved and the Germans having reached a "high water mark," it was now "anybody's war," as evidenced by the fact that it lasted four more years. In this regard, it was like the successful defense of Moscow in World War II.

Answer 2

It meant that at least one army, the first, but also quite probably the second, and maybe even endangering the severely weakened third army, faced the danger of encirclement and total defeat.

Supply lines were already strained heavily, French resistance became more staunch, the 6th French army guarding Paris more or less a surprise, and the third army being quite sick with plain illness. When Kluck stormed ahead with his first army, first too far to the South then disorganising the plan already and then turned West to attack what's in sight for him, the interlocking advance of German armies, guarding each others' flanks, was no longer interlocking, creating the gap.

The BEF moving into it almost unopposed had created the possibility of cutting off the first and second army. While the ensuing panic on the German side may have been a bit of an overreaction, completing this encirclement would have most probably ended the war a lot earlier.

_{(From: Sven Felix Kellerhoff: "Ein Befehl ließ den deutschen Kriegsplan scheitern", Welt, 09.09.2014.)}

More detail in a slightly outdated Sebastian Haffner & Wolfgang Venohr: "Das Wunder an der Marne. Rekonstruktion der Entscheidungsschlacht des Erstens Weltkriegs". Luebbe: Bergisch Gladbach, 1982. Which is the base for a nicely illustrated documentary: "Generale – Anatomie der Marneschlacht" (On YouTube). The dramatisation and dialogues shouldn't be taken too seriously, but the frontline visualisations will show you what you look for. For a more BEF-oriented outlook, of course the Wikipedia page: First Battle of the Marne is amply referenced.