Excellent call- start with The Way We Live Now. (Trollope was writing about Bernie Madoff a century before Madoff started his scams!)
Although I have studied 19th century literature at degree level, I disagree, but even if I didn’t I would feel that the the books that are being mentioned in this thread are great for a cosy evocation of an all white Britain with the aristocracy in charge, useless if you want to understand Britain in 2015.
Where in any of these books are you going to learn about the Empire Windrush and the migration of black and Asian people to Britain? Where are you going to learn about how different communities get on today? Where are you going to learn about the foundation of the NHS and the ongoing arguments over its management? Where are you going to learn about the British government’s decision to invade Iraq, or the crash of 2008?
Rather than nursing quaint romantic images of a Britain that in many cases never existed (even literature that was unromantic at the time it was written becomes romanticised if people use it to escape contemporary reality), I would suggest starting with perhaps Zadie Smith or Jonathan Coe.
For something a touch more dystopian than Wodehouse etc I’d recommend Will Self. Start with The Book of Dave.