I have been to GC LHR once and GF LHR three times in last 5 weeks and 3 out of 4 times I didn't see financial times (all three times were afternoon) and was told run-out due to strong demand ( really?!) and 2 out of 4 times I didn't see WSJ. But lots of copies of DM/Times/I etc were on the shelf.
Personally I think BA should enhance away those newspapers whose inks come off easily, I.e DM!