I didn’t try calling them to explain and debug it over the phone, just thought I would book a mobile service call (in part to see how that worked out).
The chap who came out (Torsten) was very good - he ran some diagnostics on my car from his iPhone and said everything else was ok other than the cellular connectivity, and he said easiest and most likely/simple thing wrong was a bad SIM card. He carries spare ones so it was about 5 minutes to swap.
On the Whirlpool forums there is another new LR owner who it sounds like has the same issue - certainly the same symptom - but as he already has a service request for his car open doesn’t seem able to open a separate mobile service request for hopefully the same simple SIM swap fix.
Odds are the three of us with cars in the same batch and the same symptom are more likely than not to be from the same cause...