I have definitely seen BA operating out of T3 for several years, or at least BA a/c parked there. Normally it seemed to be 747s.
However, there are definitely quite a few destinations currently served out of T3 to Spain and Italy and most probably others. Someone told me that the 757 could not operate out of T5. Before I get shot down that's just what I was told!
Certainly the 320 and 757 operate from T3 and use, ironically, old T1 stands.
ps
Groundloop: sorry should have read your post.