Thanks for your help, but there was no problem with the Guardian website as the problem occurred randomly at other websites as well. It also had nothing to do with a WiFi connection, because I was not using WiFi when it happened.
However, I think I solved the problem and want to provide a solution here for anyone who may encounter similar trouble. It seems that the popup finally went away when I deleted most of my "website data".
I originally thought it would be sufficient to just clear all "History and Website Data" in Settings/Safari, but it turned out that this does not delete the website data at all. In fact, when I go to Settings/Safari/Advanced/Website-Data, there was tons of stuff left that was not deleted yet. In fact, in that menu there is also an option to "Delete Website Data". I clicked on this option repeatedly, but nothing happened. Although the phone claimed that all the Website Data had been deleted, I could confirm that all the stuff was still there. Absolutely nothing got deleted. I then went individually through the list, swiped over every single line, and deleted it one by one. Took me almost 20 min. This way I could delete almost all Website Data. About 10 items could not be deleted, no matter how often I tried. I searched online, and this seems to be a common problem since iOS 10.3. In any case, even though I could not delete these last 10 items, the stupid popup seems to have disappeared with one of the other deleted data. At least, so far the popup has not returned for eight hours ...
