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?