Mons was a victory for the BEF.
Are you thinking of Le Cateau ?
Mons was not a victory for the British, also I don't know where Wikipedia is getting the casualties for the battles from but they are wildly off.
In reality the British lost about 1,600 men at Mons wail the Germans lost about uncaritably 1,900. Also only 2ed corps actually fought all day, 3ed dint git into action untill the break though happend and the 4th dint even get to the battlefield untill after dark. The 2hkk never made it to the battlefield because Kluck was convinced that the BEF was at lille and there for had them marching though all hell and creation trying to find them. He dint even know a battle happened at Mons untill the next day.
So there's your pod, Kluck actually lisinse to his calvary when they report that the bef was at Mons (or use his air recononsence which he dint throughout the intier 1914 campaign) moves so that his hole army is actually facing the BEF, or gust have his calvary corps swing around the completely unprotected British left sense the British calvary was bisiy keeping a tenuous connection the the French fith army on its right. And roll up the interer BEF.
Something similar could have happened at le cateau as well. Really the bef was extremely lucky that it was facing someone unqualified to monuver a force as larg as an army. Something unfortunately coman in the imperial german army during 1914.