I have exactly the same problem with a new WDTV Live SMP which I purchased yesterday.
I’ve done the factory reset of settings and reset location (confirmed to be United Kingdom) multiple times but still no iPlayer.
I did find this thread re a previous failure of WD’s location server and I wondered whether it was the same problem occuring at the moment?
My model is WDBGXT0000NBK-02 and I too have fw 1.15.10.