My situation was a bit different from yours, but what I have heard from professors at Columbia and Berkeley is that having a different undergraduate major is actually a plus for you if your statement, writing sample, and perhaps Literature GRE scores (for schools which look at those) are strong. If this is the case, then having studied something else makes you stand out to the adcom in a good way. One of my profs said that when an applicant has as strong a writing sample as someone else who studied Lit undergrad, she is more curious and impressed by the applicant, and if the applicant can spin her/his studies-in-another-area to explain how it might inform their interest in literature, they actually have a significant edge over other applicants.
If you wanted to have more coursework in English lit, and you still live near your undergrad institution, you might email some professors in the English department and ask to audit a class or two. Building good relationships with these professors might help you in your application process--they might end up writing your recommendations!