Well, if you go to the Great Circle Mapper, you'll see that the flight path doesn't go that far into the arctic circle... so yeah, you should see sunset, probably around 10pm local time, which is about 6 hours into the flight as dll said. However, sunrise at LHR is at ~4:45am tomorrow so you should get some sunlight for the last couple of hours.

(Night may not be totally dark, either, i.e. you will probably see at least a faint glow to the north... but this is just an educated guess, I haven't actually flown this route.)