The timing of the Haneda longhaul "window" makes scheduling of flights from the UK particularly difficult.
BA currently operates close to the end of the window, but still departs from Heathrow too early for feeder connections from elsewhere. Departure from Haneda is also uncomfortably early, but not quite early enough to make it worth saving a night in a hotel. Moving to early in the window might make it more user-friendly at the Tokyo end, but would involve a night departure from London.
Peter47's idea of a plane on the ground at Haneda all day could ease the timing problems, but even retrieving a 747 from the desert might not make it economic.
Another alternative, which also has drawbacks, would be to introduce an intermediate stop in somewhere like Seoul. This would probably permit an evening departure from London, arriving at Inchon (Gimpo would be better for Korean domestic connections, but is probably not acceptable to the Korean authorities) in time for a late eveing departure to get in early in the Haneda window. Return might be possible early enough to save that night's hotel in Tokyo and still arrive back in Seoul late enough to avoid any night curfews.
Obvious disadvantages are that the flight to Tokyo would no longer be non-stop and picking up passengers for the Seoul-Tokyo and return legs might difficult both practically and legally. However such a routing would introduce a British presence onto a route where there is none. It would also increase One World presence in an area currently well-served by Sky Team and *Alliance, but only by Finnair from One World.