Is the train a lovely way to go or should we just fly and get to London as quickly as possible?
Train, city centre to city centre it is quicker, only 4½ hours with departures every 30 minutes. It is also a lot more comfortable, no trip to and from the airport, no check-in, more room, just one seat ride. You can get up and walk around the train. There are some scenic portions, particularly the northern part of the route.
Tickets start from £25 if bought far enough in advance, a lot more if you buy on the day.
Fares and tickets from the railway company here: https://www.virgintrainseastcoast.com/
Take the train. (You might want to break the journey with an overnight stay in York - if so, you would need to purchase separate tickets for each leg. www.nationalrail.co.uk is the easiest way to find the schedules & fares - although it is only Virgin Trains who operate the through services. Other companies also operate London to York and York to Edinburgh).
This shows you the route in reverse - check out the video at the end:>https://www.seat61.com/london-to-edinburgh-by-train.htm
I've done that route a few times. Besides all the reasons mentioned, there is no security to go through. Just show up a few minutes before the train leaves and board. (You might actually want to give yourself more time that just a few minutes.)
The scenery is mixed. Total travel time will be about the same. However, in my opinion, the train is less of a hassle.