I know there’s some other forum lurkers who’ve been having the same problem, so..
The first dongle I bought just displayed the message “Internet may not be available” when I tried to set Chromecast up, and then just returned me to the beginning of the cycle. RATS!
So I thought maybe there was a manufacturing fault with some batches (a bit like Endura winter gloves) so I did an exchange for a new one.
The new dongle displayed “Make sure your Automatic WiFi enabler is turned off” – that is to say – on your mobile device settings.
Hey presto. 😀