OK, here's the problem. If you clicked anywhere in the pop-up the first time it appeared that ran a JavaScript object that essentially linked the malware to your browser so any site that you open after that will display it. CNN, Fox, etc, are not really at fault here. You need to stop the process in its tracks. To do that put the phone in Airplane mode, open Safari and close all open tabs, then go to Settings/Safari and clear your history and website data. Sometimes it helps to turn off JavaScript (temporarily). Turn off Airplane mode and go to some "respectable" sites. Assuming it's OK, turn Javascript back on and try again. This will probably fix it. If it doesn't there are further steps, but usually they are not necessary. Before you go back to the site where it first appeared install a good ad blocker.
It's been said before in this thread, but Apple's pop-up blocker actually works, but these ads are not really pop-ups. They are redirected web pages that are designed to look like pop-ups, to get around Apple's pop-up blocker.