Oooh yeah, I hear Handmaiden's Tale is exemplary. Also, Pillars of the Earth.
Forgive me if my thoughts are a little all over the place, and please feel free to ask for clarification if they are.
My first recommendation always is and always will be Wuthering Heights, followed by To Kill a Mockingbird (although that's more for the US). The Kite Runner is beautifully written, although some prefer A Thousand Splendid Suns. The Book Thief was amazing as well, but terribly *heavy*. The Picture of Dorian Gray is phenomenal and so is Count of Monte Cristo, and neither are overwhelming in any way. Tenant of Wildfell Hall is a good girl power book.
I really enjoyed Manhattan Transfer. I did not particularly enjoy The Sun Also Rises, but it's definitely worth a read. The Sound and the Fury is a very, very difficult read, but SO WORTH IT. It's life changing.
If you're into plays, don't pass Hamlet up. Best play ever.
I do not suggest A Song of Ice and Fire wholeheartedly - I have many reservations about the way it is written, although the plot is decent.
I just finished reading The Handmaid's Tale. It's a satire of feminism. Thanks to the extremists, the US has turned into a dytopian society where women are "protected" from the outside, and are used to strictly procreate. Quite an interesting book, I'd say.