Should have built a conventional railway London to Birmingham. Probably using part of the GC route. Spend the money saved on reinstating the slow lines on the ECML and other route upgrades.Laying all the track on a concrete slab must have pushed up the price.
Bit in bold Not sure how that would have worked though ?
At the London end you'd either have been trying to get out of Marylebone or use the New North West line and run up through High Wycombe - a line which doesn't have much spare capacity, has a lowish linespeed and no chance of being 4 tracked without spending the GDP of a small African nation.
Further up, I've walked bits of Northants where the GCR used to run, to pretend it would be somehow easier and attract less opposition than the HS2 route has is for the birds quite frankly. Places like Woodford Halse would have been sliced in half and lost a woodland area which the village consider an amenity. It's really not helpful to pretend that just because it was once the course of a railway line, rebuilding along there would somehow be cheaper / easier / quicker - it really wouldn't.
Then you have to face up to the fact the GCR ran nowhere near Birmingham - perhaps the reason HS2 hasn't taken more of its formation - it headed North-East towards Rugby and Leicester. You'd have come into Rugby facing the completely wrong direction to then try to head towards Birmingham along the Coventry corridor, so realisitcally you'd have had to start deviating from the GCR formation in the Catesby area and then heading North West towards Southam, Kenilworth and Balsall Common to serve Birmingham Airport - which is basically what HS2 is doing......
And what "slow lines" are these that need "reinstating" on the East Coast Mainline ?
Lastly, why do you think concrete slab track is more expensive than laying concrete sleepers and 'loose' rails ? I suspect the difference isn't as big as you think it is and for +140mph high speed, rigidity of the track is of greater importance and has to be engineered to a higher standard than 100 mph.