The whole GCML so as to relieve stress of WCML
We shouldn't go back over this, but...
The GC doesn't exist any more. It's gone. Some of it is a very well run tourist attraction. Half of it has been built on. Some of it has been bulldozed into the ground.
Where does it go? You'd need to quadruple half the southern end of the Chiltern line to get even an ounce of capacity you'd need. There are nowhere near enough platforms (or space to build more) at Marylebone. You'd need new platforms, stations and rebuild half the line.
It doesn't go to Birmingham. It goes to Rugby, Nottingham and Leicester. That's not relieving capacity issues on the WCML, that's helping capacity along the MML.
It's not build to modern standards. There a lot of quite sharp bends you'd need to rebuild, and the capacity from a sawtooth speed profile (lots of speeding and braking) is significantly less than that from a relatively steady speed profile.
You'd need to rebuild the line completely to modern standards, and that means having to buy the land back. All the land. That's going to cost about as much as building the line across greenfield sites. And, if you're going to rebuild the line completely, and buy back the lands you may as well build the line in open countryside, instead of through the centres of some quite large towns.
Basically you don't get anything more from rebuilding an entirely demolished railway line than building a new one in open countryside. You can make a faster line, straighter and more optimised for fast trains. HS2 serves where people want to go. It serves bigger cities and relieves a busier main line. It's faster, straighter, and in all honesty probably a similar price.
The Great Central has gone. Rebuilding it doesn't gain anything that HS2 doesn't do better. It should stay dead, a regrettable loss, but a loss that is permanent.