Put that onto the East Coast Mainline and you have direct competition for the airlines in terms of time. Flying Edinburgh to London is about 1 and a half hours flight time, add an hour for the check-in will give you two and a half hours.
Currently by train from Edinburgh to London is between just over 4 hours to around 5 and a quarter hours, depending on the stops and time of day. With a near doubling in the speed of the train, over the majority of the route, this could give journey times of around 2 to 3 and a half hours. Of course this would require a raising of the current 125mph speed limit on the majority of the line.