Thank you - you really ARE a star!
Now why didn't I do that in the first place? Because it seemed too obvious I suppose, which just goes to show that the simple answers are usually the best.
When I said OK to setting up one of the channels as you suggested, there was a very brief flash of message saying 'you're setting up channels you've already subscribed to' but it disappeared before I could read it all, then the picture came on and the recorded boost items, live and recorded, are now available.
Pity the helpline person didn't suggest it - I thought it was silly to say the box was at fault, otherwise other things would surely be wrong as well or it just wouldn't work at all.
Once again, thank you very much for your help and hooray for the Community, proper help at last.
(I'm posting this as an accepted solution because it has worked but don't know what TKB is...)