Perhaps the question is less what new railways should we be building in London, and more is it sensible to keep concentrating all economic growth there ?
This is pertinent to the "what are the railways for" thread - are the railways there to deal with actual demand (i.e. mass transportation is going to be more efficient in areas of heavy population density in significant urban areas, and less efficient on rural branch lines) or are the railways there to shape demand (in a kind of "If You Build It They Will Come" / SimCity way)?
Maybe if Milton Keynes (the flagship "new town") had been built around the GC route (rather than on the WCML) the line would have been saved, but what happened happened.
The underwhelming frequency on "non London" routes (e.g. only hourly from Birmingham/ Leicester to Peterborough/ Cambridge, only hourly from Bedford to Bletchley, only every forty five minutes from St Albans to Watford) make me sceptical about how busy a new (or reinstated) line would be - Rugby to Leicester would certainly have its uses if around nowadays but how much would we have to pay for that privilege (when we don't have the money to wire the MML)?
Keep it simple. Wire the MML and give us some proper length trains (rather than four/five coach 222s).
If we ignore the social use demands for the Hope Valley I think the Woodhead would be the one retained, and we would have to wrangle a route north out of Sheffield Midland to the Woodhead route
Even if there's space to climb from Midland Station (which was built directly above the River Sheaf, i.e. bottom of the valley) towards the Woodhead line (e.g. the height of Wicker Arches), the line further west would be too much of a bottleneck.
You've got half hourly stoppers from Dinting to Piccadilly taking around half an hour to cover a dozen or so miles, with no easy room for overtaking (little scope speeding them up as 323s are about as fast accelerating an EMU as there is), so any services from the Woodhead line are going to be severely constrained.
Whereas the four track through Stockport mean that the current Sheffield - Manchester services can be segregated from "local" trains.