ABO944:
If you want to check approximate routes across the pole try this link, where you can just put routes in such as your LHR-NRT example here (which you will see just runs across the north coast of Siberia rather than over the pole.
http://gc.kls2.com/cgi-bin/gc?PATH=LHR-NRT
IIRC the most likely to go overhead the Pole is the Continental flight from New York to Hong Kong westbound (eastbound it tends to be down over Alaska). In summer it's daylight all the way.