Finding just the right topic is one of the most common struggles with research in any subject area, and it is particularly troublesome to literature students because there are so many potential subjects on which to write. You mention English literature, so that does narrow the field a bit, but there are still so many choices.
First of all, it is important to select a work that you particularly like or that you find particularly interesting and would like to know more about. You will be spending a lot of time on this project, so it is always better to select something you will be able to maintain interest in. If you enjoy poetry, choose a poem; if you enjoy drama, choose a play; if you enjoy fiction, choose a short story or novel. Your selection must meet the guidelines of the assignment, of course, but it should also be something interesting to you.
In terms of what this kind of research entails, I have attached a great eNotes site on how to write an English literature essay. It shares something important about the kind of work you will be doing for this paper, at least based on your description of the assignment. In part it says:
You get [understanding] by reviewing the work closely and repeatedly, and by looking at content, form, and function. [E]xamine each choice made by the author until you can explain how it relates to the whole. Slow down, and take all elements of the work into account: sound, shape on the page, structure (chapter length, number of chapters, etc.), point of view, and so on.
Finally, the Purdue site I have attached will also give you some specific ideas about the kinds of topics which you will probably find helpful. Perhaps you can do a character study, such as comparing the sisters in Pride and Prejudice or examining Hamlet's indecision in Shakespeare's Hamlet. You might look at a text from an historical perspective, such as the conditions in England at the time of any of Dickens's writings, or how a specific time period impacted an author like Thomas Hardy. Another idea is to compare and contrast one work with another, one character to another, or one work to history.
It's really difficult to suggest any specific titles for you, since so much of literature study is based on personal preferences and what you have and have not read; and your selection has to suit your professor's assignment and the length of the paper, as well. I would simply encourage you to think specifically about whatever work you choose. For example, rather than saying you are going to study Hamlet in Hamlet, you should focus on one aspect of his character and how it is displayed in the play, like his acting, his indecision, or his relationships with women. Again, choosing your topic is crucial, so consider what you like, what you've read, and what your exact assignment is before selecting anything.