I used to pax LHR-LAX over the years going out for Christmas, thus around this time of year (including leaving London a few hours before Pan Am 103 was destroyed in 1989 and arriving in LAX after the flight to all sorts of concerns from those back in the UK who knew me but not the detail of my plans).
Yes it does get dark in the middle of the flight, almost imperceptebly. If you leave at lunchtime it seems to get slowly dark when your body is expecting sunset by UK time, so does not seem unusual, it then very slowly gets lighter as the flight starts to dip south again. But there was always some glow in the sky to the south.
There was often the sort of red tinting of any banks of cumulus underneath that you can get at sunrise/sunset, on one trip this was spectacular and lasted for hours, from Baffin Island to beyond Winnipeg.
In the days of prop aircraft in the 1950s this was a significant difficulty for the pioneer polar flights (eg SAS DC-7C Copenhagen - Seattle - Los Angeles) as they were still reliant on astral navigation, and they spent many hours when going west with the sun just below the horizon (so no fix on it) but the sky not dark enough to see the stars. There was an instrument eventually devised to overcome this, others may have more detail.