Wouldn't a more sensible option be to develop a direct high speed link along the East Coast Railway line to one of the many airports along the route, particularly somewhere like Doncaster for instance.
With the right train you could be in side the terminal in little over an hour, have check in services in the railway station in London with baggage drop for people who have an evening flight.
Something similar to the Hong Kong setup.
A) Would generate jobs up north
B) Would reduce the amount of air traffic in the South
C) Has lots of room for expansion.