Cloaky was the culprit for me! Updated the version of Cloaky installed and everything is back to normal. My iPad is also jailbroken but doesn't have Cloaky installed, hence why it was still working when the iPhone wasn't. Thank you sooo much SamG!
I've been having the same problem since yesterday, but only on my iPhone. iPad and desktop apps are working fine. I started by forcing closed and reopening, and have progressed through uninstalling, turning it off and on again, hard-rebooting and reinstalling, and I can get no further than an unresponsive sign in screen. Very frustrating.