1) Dee Brown - 'Bury My Heart At Wounded Knee'.
I recommend this largely because of Jon Cruddas' recent speech mentioning the book 'Radical Hope' by Jonathan Lear. That is a fine book with good insights, but this one has much greater depth of history and background on the existential and material dispossession of the American Indians, with moments of joy and hope across the cultural divides. It helps to break down what is good and right in amazing, diverse, confusing situations.
2) J.B. Priestley - 'English Journey'.
A travelogue across England published in 1934 during the Great Depression. It's a really easy, pleasurable read from a writer who can express himself in beautiful language and who doesn't hold back from righteous anger and despair when he sees what is happening in various places. It also makes you aware that, far from what many politicians like to say about us 'living in a new world of change' and suchlike, what we are going through is nothing particularly new - mostly just extensions of what was already happening back then.
3) Chantal Mouffe - 'On the Political'.
This short, accessible book provides a jolt to our conventional thinking on the left. As she says: "Politics is about the constitution of the political community, not something that takes place within it." This is about seeing politics as a public space, rather than a protected space which works to exclude many views and many people. She is tough and challenging and well worth reading.
4) Bethany McLean and Joe Nocera - 'All The Devils Are Here'.
The best book I have read on the origins of the financial crash. It's detailed, punchy and readable. It focuses almost entirely on America, but deals with the micro situation on the ground with dodgy mortgage brokers as well as the bigwigs at the top. It'd be great if we had anything similar about the workings of the City of London.
5) Karl Popper - 'The Open Society and Its Enemies' (Part II on Hegel, Marx etc).
Immensely readable philosophy that destroys Hegelian historical theory and scientific Marxism but shows great sympathy and love for what Marx and Engels did in exposing the disasters and hypocrisy of early capitalism in Britain. Popper gets carried away with his rhetoric at times, but his reasoning is sound and his writing accessible and enjoyable for the general reader - a world away from most philosophy in its ivory towers.
Addition: It was a bad error not including this book, so five books must become six.
6) David Goodhart - The British Dream. Successes and Failures of Post-War Immigration
This is a book about the here and now, and all lefties should read it if they possibly can (even just the introduction if nothing else). Goodhart's thoughtful analysis is nicely readable but dispassionate, intelligent and sympathetic to all sides of the immigration situation. But it is also challenging. By taking on liberal-left group-think he has drawn a lot of abuse and criticism, and that makes what he says all the more welcome and important. He doesn't get everything right, but no one possibly can when taking on an issue that is so loaded with political ideology and the politics of silencing and shaming.