In addition to coldtea's excellent list, there's a handful of modern novels that have always stood out for me over the past 30-40 years of reading:

The Testament of Gideon Mack: https://www.amazon.co.uk/dp/014102335X

Hard Boiled Wonderland: https://www.amazon.co.uk/dp/0099448785

Walking on Glass: https://www.amazon.co.uk/dp/B002TXZTE8

The Ginger Man: https://www.amazon.co.uk/dp/0349108757

Perhaps not true cult classics, but they're often titles I've recommended or just buy for friends many times, and go back and re-read periodically.