So I’m at Heathrow and the WiFi fan is showing on my iphone but it says there is no connection. ????

Many free WiFi hotspots require you to go to a web page and click on accept button before the WiFi works. Open up you browser and see if it takes you to a sign in website.

You probably need to pay before you can be connected. Go to Safari and see if a login page for the WiFi point comes up.