This method solved it instantly for me...
Settings > Safari > Advanced > Website Data > swipe left on the trouble website to delete
I had tried clearing browsing history multiple times, rebooting the phone, etc, to no avail. Deleting the trouble website from “Website Data” fixed it right away. I didn’t delete any of the other websites except the one that kept having the pop-up...for me it was www.bbc.com.
FYI, my phone is iPhone 6 on iOS 11.1.1