I think I know what the problem is.
Some time ago I read that each time the iPhone connects to a wireless network, it connects to a server URL apple to make sure the wifi network is free and does not require further authentication at the router (eg WLAN no password but with internet charges).
Apparently this page of the apple server is not reachable at the moment, and the iphone believes then you should login to the router (and this shows the page that says "the page you're looking for, etc. etc.").
The only thing we have left to do is wait for Apple to solve the problem at a server level.