Ok, so when I came home the outage was resolved, but I disconnected the Internet node to simulate the problem.
Pushing the Connect to hub under Tools only sent me to the subscription page.
After some fiddling with the WiFi-settings I found the solution.
My router has the option to create a secondary SSID and the settings on my phone was to auto-connect to both that and the primary one. This caused the connection trying to resolve Internet access by circling between the two SSID's.
The concrete solution was to remove auto-connect from the secondary SSID and having the phone accepting to use WiFi without Internet access.
Thanks for the support guys!
Even if a direct solution wasn't given you made me think in new directions, which was a solution in itself!