Thanks Graham. I bit the bullet and did the factory default reset. Went well. I found a good S & Q signal at both tuners, connected with 2 cable (sic), but only for the same channels which I had before. The ones which were "missing" are still so - No Signal at either tuner, but still shows as 2 cable.
Peculiarly, the TRUE channels reappeared but when (out of curiosity) I had a look at signal info for one the little picture went blank and the No Signal indication returned. Afterwards, none of these channels was accessible.
A couple of things I have noticed since the reset is an advert for Freesat App for mobiles that appeared before accessing the Recordings screen (don't remember seeing this at previous initial setup), and the font for the channels list (but not the programmes) in the EPG looks different. The latest software update is dated 20 JUL 2015, shortly before my problems started - could this have some bearing on the matter (though, if so, I guess other people would have had similar problems).
Otherwise, I guess I will have to somehow try testing with a good box/feed setup to diagnose where the problem actually lies.