The Flying Scotsman used to leave London Kings Cross (KGX) at 10:00, but this has not been the case since the Eureka timetable was introduced in May 2011. The Flying Scotsman is now the 05:40 East Coast service to London Kings Cross, calling only at Newcastle and taking exactly four hours.
I was actually looking at some old GNER timetables earlier on today thanks to the Wayback Machine. I noticed that the Flying Scotsman used to depart at 10:00, and the Northern Lights service to Aberdeen used to depart at 10:30.
However, since the introduction of the Eureka timetable, the service pattern for Edinburgh services (from KGX) has been as follows:
Top of the hour: Fast service to Edinburgh: non stop to York, then calling at Darlington, Newcastle, Berwick and Edinburgh (with a few extensions to Aberdeen, and one to Inverness and Glasgow).
Half past the hour: Slower service to Newcastle: calling at Peterborough, Newark Northgate, Doncaster, York, [Northallerton every two hours- I think], Darlington, Durham and Newcastle, with extensions to Edinburgh several times per day, calling at Alnwick.
I'm guessing that as both the Flying Scotsman and the Northern Lights are express services, they were unable to fit them both in the Eureka timetable within the same hour. There would have been too many stops for the Northen Lights to run at half past 10, but they wouldn't want to spoil their clock face timetable. It would have been impossible for them to make it run immediately after the Flying Scotsman as there is a service to Leeds at 10:03, and a stopper to Newark at 10:08.
I'm guessing that this is the reason why the Northern Lights has been moved forward to depart at 10:00, so as to fit in with the clock face timetable, and the Flying Scotsman name is now given to the completely different service.
I think it's a shame that they have broken the tradition (although I can see why they have done it), and also agree that there should be a northbound service.
I hope this long post has been useful: I am typing this on the iPhone app and went to double check East Coast's timetable, and when I went back to the app, I had lost everything, so I have typed most of this out twice!