Well an English literature degree isn't going to teach you to write, although it will give you exposure to a lot of the literary substrata which will invariably influence your work as a writer and allow you to formally analyse it (and by extension, your own work - and understand how your work may be received by others).
If you mean an English language or creative writing type degree, then the benefits are probably more that it provides a structured but relatively "safe" environment (financially at least if not critically) to workshop ideas and start developing what might later become a published work for you. If it's a good course it will also provide networking opportunities to become familiar with established writers who may be able to help provide guidance or support, and ideally also insight into the publishing world and what publishers look for (and where and how you should be putting your work out for publishers to see).
It doubt it's a magic bullet situation where it makes or breaks anything - plenty of writers succeed without doing any degree - but can provide smaller incremental benefits and insights that will make breaking into things less arduous potentially.
If you're just doing it to go through the motions of getting a degree because "that's what writers do" then you probably won't get much out of it anyway though.