I quite like the idea of English Literature being...English Literature! We have such an incredibly rich history of writing. I did GCSE and A Level Eng Lit, and can't remember which texts were for which, but I did Far From the Madding Crowd, Wuthering Heights, possibly Jane Eyre (or that may have been pre-GCSE).
We had equal weight to prose, poetry and plays, so I studied a lot of Shakespeare throughout secondary (Twelfth Night, Merchant of Venice, Antony & Cleopatra, Julius Caesar, Midsummer Night's Dream, The Tempest, all great stories. This are the ones I remember), and a variety of poets (Keats, Larkin, Heany, Blake off top of head).
TKAMB is definitely reading for enjoyment rather than analysis IMO, but it's a book I have really enjoyed, and think its relevance is great perhaps for reluctant readers? I was a really avid reader, and my school expected us to read widely. I also recall doing independent research on DH Lawrence and Thornton Wilder, not sure if that was for coursework maybe. And I adored Orwell (and am introducing my 11YO DD to Animal Farm soon, after discussing it with her this week and her saying she really wanted to read it).
I think other English writing (I guess I mean non-UK) is great too, but when our UK authors are studied all around the globe, I think it's important we learn about them too.