Does failing a module affect applying to masters?

I am a first year student studying classics at UCL. I am now struggling with one of my modules which requires two pieces of essays. I got one essay with a high 2:1, but I was experiencing a mentality breakdown, time management problems and family problems when writing the another one in the past few weeks. I submitted the essay so late that it was capped at the pass mark, and it was hugely under the word limit (for 500 words). I don’t believe I am incapable since I have been done pretty well in other modules, it is just these few weeks that have been hard and peculiar. I can legitimately forego that module since UCL only take 3 out of 4 course units into account. I would like to know, if I fail and retake it, does that affect my master application to other places (e.g. lse and Cambridge) provided that I got a first in the end? Will that hamper my career by much? Thank you!