Judging by the current options presented at qatarairways.com whereby only BA (not QR) is generally offered at any sort of sensible price for the DOH-LHR segment of a CAI-DOH-LHR itinerary (and presumably other XXX-DOH-LHR itineraries) I would say that low demand might indeed have something to do with it.

In fact, given the frequency with which QR (a OW alliance member) flies DOH-LHR-DOH, I don't know why BA doesn't drop the route altogether.

Incidentally, a polite reminder that posts on the FT BAEC forum stating that QR is better than BA (or indeed any discussion about QR) are frowned upon in certain quarters.

Foxtrot Oscar - assuming you're flying J, it's your lucky day. QR 380 v BA 777 = no contest.