Just to help close this out.
It was saying October in the app in words, and given I'd only picked it up on Thursday, Iwas fairly confident that it still had 28 or so days left. ;-)
Tesla support line would also appear to be closed at weekends as well, unless you're dealing with a genuine emergency and this clearly didn't feel appropriate for me to try and justify to them that it was....
It's a tesla direct lease, and I actually had the option to setup and subscribe to premium ready for when it expires within the app - so did that, and while the car restarted itself and now showed premium connectivity again. I was still unable to use netflix, YouTube and was getting the connect to wifi message (and was happy I was in a good signal area, as I had the LTE displaying and 3 bars).
Despite the standard restarts not working, tried a shutdown at this point from within the screens.
And hey presto, it appears to work now. So not sure if it's that shutdown that resolved it, the subscription (albeit with a delay). But just glad to have it resolved - especially as we're on the mandatory demonstration tour around friends and family!!