But I guess there are some books that are so basic you are sort of expected to have read them. Not 'what books are best', it's 'what books do you need to know about in order to participate in educated society'.
So, I think you can be 'expected' to have read (or at least know all about) books like Alice in Wonderland (and Through the Looking Glass), A Christmas Carol, Pride and Prejudice. Lady Chatterley, perhaps, so you know what all the fuss is about. The Bible ditto. There are a few plays - Hamlet and Macbeth, possibly The Importance of Being Earnest and Peter Pan - you ought to know in general terms. A few poems like Kubla Khan and The Daffodils.
ETA - I just thought - 1984 and/or Animal Farm.
I think in America there are different novels with that status: the two I really notice that Americans talk about are Moby Dick and Tom Sawyer. Wizard of Oz perhaps? I think you could get away with knowing nothing about them in Britain. I don't have a clear idea about 'essential reading' in other countries.
There are also books you need to know about to participate in a particular community, such as the SF novels 'everyone has read'. These are also different between countries: few Brits read Heinlein, but I think most have read Arthur C Clark.