While most U.S. Universities have strict deadlines for applying, most UK universities do not seem to mention any deadlines for applying on their websites. Why is this? Or am I mistaken? Before what date should I apply?

you can sometimes find deadlines on the pages of the individual departments rather than on the university pages, as they vary.

most departments i know of have rolling applications, that is, they take new students until they are full. some will have a deadline at which time they will start looking at the applications. this will often be in january, sometimes already in december, sometimes later. in popular courses it is necessary to have your application in by that time, since after this the course will invariably be full. but, if the deadline is jan 15th, it doesn't matter if your application gets in in october or on jan 14th. in less popular courses you can easily apply later, and still have chances to get in as late as july. however, chances decline the longer you wait, and further, you will lose chances to apply for funding.