Dan, as you can probably guess there is an immensity of contemporary classical chamber music to explore. I agree with Duncan about Shostakovich being a good starter if you like Britten and Kabalevski (Prokofiev proves a bit more difficult for many, myself included). Schostakovich's chamber music is anchored by his 15 quartets, the worst of which are merely very good and the best of which are sublime. There are many renditions: my personal favorite is by the Fitzwilliam quartet, but the Emerson and Borodin are also very good, and there doubtless other greats that I haven't heard.
By the way, if you're buying classical music, cost is pretty much a non-issue if you're willing to look around and use eBay. Classical CDs and LPs go for so little on eBay that it's a cultural embarassment (not that I'm a snob or anything
). I just hopped over and looked for S.'s quartets, and sure enough, the complete Fitzwilliam quartet set on 6 CDs just sold for
$12.55. Incredible.
There are so many other things from Shostakovich's hand alone that it's hard to narrow things down, but since you mentioned cello explicitly either of S.'s cello concertos are very good (the second is better, IMO). And there are many other contemporary composers routinely buried beneath the endless Beethoven/Mahler/Rachmaninov worship. A handful of noteworthies include: Alfred Schnittke (a brilliant, more radical, and younger version of Shostakovich), Bela Bartok (quartets are also brilliant but more challenging), Paul Hindemith (close to Britten in many ways), and Kryztof Penderecki (very exciting contemporary Polish composer: second cello conterto is a good starter).
Anyway, I'd say start with something like Shostakovich's quartets, or one of his other chamber works, and listen to them for a few months.
Cheers,
Eric