Normally I have WiFi running (and connected when when at home and at work, on the guest network) along with 4G. The other day I was shuttling from one work location to another (so 'lost' WiFi) when I found a bunch of apps that wouldn't work. Twitter said 'No internet connection,' Life360 said 'Check your network connection,' LinkedIn would not connect, Google Play said 'No internet connection. Make sure Wi-Fi or cellular data is turned on then try again, " etc. Well 4G/cellular data WAS turned on so I wasn't sure why I was seeing that error message! I checked all my data settings, rebooted, etc. No joy!
At work they have changed the guest network WiFi - now after connecting you have to launch your browser and acknowledge some use language. You don't have to do this all the time, only every few days. The other day I couldn't get connectivity and all these apps were "dead" for all intents and purposes! Turned out WiFi was showing "connected" but i hadn't gone to the page to re-acknowledge; as soon as i did that i was OK!
The bottom line: when I had no more WiFi my applications wouldn't just automatically continue to work using the 4G data connectivity, they all just say "No internet access". Shouldn't this happen/switch over seamlessly (i.e. if an app is connected via the WiFi network and loses WiFi connectivity, shouldn't it just stay connected via 4G?). I twigged to this when I turned WiFi off and they all started working immediately!
P.S. The only place I am aware of where I have specified to use WiFi only is in Firmware Update(i.e. only check using WiFi network)
EDIT: Found an "Aggressive Wi-Fi to Cellular handover" in Developer Options, so have checked that to see if it helps....