This list annoyed me when I first read it 3 years ago, and it annoys me even more now. So many of these texts need the study that you can only give them while in University. It's such a random list as well... The books you've read before you go to Uni don't matter - it's HOW you read them. What's the point in reading To the Lighthouse and not understanding a word of it? Unless you have some kind of photographic memory and you can remember everything you read, I don't understand reading the bible before you start your degree either - you're not going to glean anything worthwhile from it that most people don't already know. (You should have a basic knowledge of the stories within the bible that most people already have a basic knowledge of anyway). If you've never studied Modernism before, you probably will not have a clue what's going on in Woolf, Eliot and Joyce. They are difficult writers. Unless you're seriously interested in texts pre-Shakespeare, you're probably not going to need to read those beforehand either.
Critical thinking and literary analysis is more important than the sheer number of books you've read. The historical context in which something was written matters - Jekyll and Hyde is an interesting read that becomes even more interesting when you realise that he wrote it at the end of 19th Century. When you start to associate the text with decadence and the middle-class fears surrounding the degradation of society because of ideas like evolution, degeneration, the fear of the city boosted by things like the Ripper murders etc, you see how important a text it is as an example of fin-de-siecle fiction. When you are constantly aware of the feminist issue when you're reading To the Lighthouse (it was written a year before women aged 21 were finally granted the vote), then you can appreciate the book more than if you just read it thinking you were going to get a story. There is no story. The narrative style is what you need to pay attention to.
Universities offer vastly different texts... I suggest reading as much as possible, as widely as possible, to see where your interests lie. The list at the beginning of this thread jokes about missing out the latter half of the 20th Century - this is a serious oversight imo. There are also only English writers...? I guess that's since it's for English Literature, but if your course only teachers English writers I find that weird. American writers and postcolonial writers seem like a HUGE blank from this list.
Sorry for the rant, I just remember reading that list and thinking "Holy shhh... I have to read all of these texts before I even start? Will everyone have read them but me?"
No. The answer is no.