Someone stopped me in the hall at church to ask which books she should read for a basic grounding in English lit. The quick answer, should you be feeling a similar deficit, is "anything famous that that has been made into a movie multiple times."
In general the "canon" of English lit has stayed 90% steady for the last hundred years. Certain things considered "must-reads" come and go, depending on the political climate in academia (when in doubt, veer sharply left). For all that I got my undergrad degree at wild-and-crazy Cal Berkeley, their English major at the time was highly canonical. Not so my husband's English degree from University of Washington. If there was some newly-popular, third tier work, he'd read it, while I'd been hanging out with persistent dead-white-guys like Dickens and Shakespeare and Wordsworth.
The summer after our first year in the Stanford PhD program, we were required to take our "Quals." The oral qualifying exam was both a form of academic hazing and a quick and dirty way to fill in any gaps in our knowledge of 500+ years of English literature. You would not believe how much we all read that summer! Hundreds and hundreds of pages and hours and hours. If you didn't end the day with a piercing headache, you felt guilty. It was awful because of the looming deadline, but wonderful because you were forced to read all those things you thought you ought to read but had never gotten around to. For some this was Spenser's FAERIE QUEENE; for me it was MOBY DICK. (Imagine my dismay, when I just checked the most recent Quals reading list online and discovered current students could choose between MOBY DICK and "three major shorter fictions (e.g., Billy Budd, Benito Cereno, 'Bartleby the Scrivener')"!) Lightweights!
Anyhow, if you're looking to shore up, go see a few Shakespeare plays and start your reading with 19th century British novels. We can argue about it, but I don't think the Americans compete in 19th century novels, with the exception of Twain and Melville. The 20th century is a different story. And we'll talk poetry another time.
Or, if you're feeling ambitious, you can check out Stanford's current quals list: http://www.stanford.edu/dept/english/deptWebFiles/forms/qualreadings.pdf