Well smoke me a kipper.
I am absolutely gob-smacked and not a clue what to do next. At least I have confirmed it's (probably) not the box.
I did a full strip-down of my (admittedly temporary) Qumi-Humax install, and took the HD-FOX into the living room where I plumbed it in in place of the HDR-FOX, ready to do the multiple reflashes etc etc as mentioned above and having already downloaded 1.01.12 and re-downloaded 1.02.20, complete with aerial lead to do the rescans necessary after restore system defaults.
Turned on, and thought OK, lets just check (still on 1.02.20)... and damn me if the portal didn't start up straight away! Had to go through the T&Cs screen, so I thought OK, maybe it has to have an aerial for initial set-up to detect that it is in the UK and therefore permitted to access iPlayer. So I unplugged the aerial and sure enough, the portal continued to work.
Fine, saves a lot of bother then. I just spent half and hour re-integrating the Qumi-Humax install, more tidily and less temporary this time, got everything hooked up and the network cable plugged in... no portal!!!!!!! FFS.
Other than a lack of an aerial, I cannot fathom what the difference is. Different viewing device on the end of the HDMI? Different Ethernet wire?? I thought maybe the HDR was completely off-line rather than standby, so I tried that - nothing.
At least I know it's not the box per se. Having put everything back and tidy I am not about to pull it all out again tonight. Going to bed to watch Holy Flying Circus.