UK (and most of the rest of the world for that matter) is a different case because the same Apple hardware can run on all 3 of those carriers. The current iPhone could sort of run on T-Mobile but would be without 3G, and it won't run at all on Verizon or Sprint. So it's not just a matter of the US exclusivity deal ending- either Apple must release new hardware specific to those carriers' networks or those carriers need to adopt AT&T's 3G GSM network standards.
But yeah, when (if) the AT&T exclusivity deal ends in the U.S. and Apple releases new hardware compatible with other U.S. carriers' networks, then I anticipate a lot of defection as customers choose the network which serves their needs best rather than being forced to the one network that has the iPhone hardware they desire. Me? I'm pretty happy with AT&T, but would love to offload some of the data network congestion to Verizon.
I predict the AT&T exclusivity deal won't end until Apple is ready to release an LTE version of the iPhone and AT&T and Verizon both have LTE networks up and running (in at least 1 city each). That way Apple can have just 1 device for both carriers, which seems to be how they prefer to operate.