Are you using WP8.1?
I think we had a clue, but need more information
Did you try to turn off speed mode?
I can't log in to many sites after the latest update. I have Nokia Lumia 925 (so WP 8.0, I guess). It's frustrating, and I hope it will be fixed soon. Also, now I can't anymore open pages in tabs when pressing links.
It works well on win 8.1 without any problem, i use it from its beta version and didn't face any problem yet, I can login on any site using speed mode and also without speed mode, try reinstalling uc then may be your issue will gone....
try disabling your addblock(atleast disable filter page adds option) in uc browser. then if problem still presists then let me know