I assume you mean an underground through station, built in a box between Chester Road and Outer Circle.
I don't know about the topological nature of the land here, so I'm going to assume that there wouldn't be any issues with a TBM under London Zoo, however, I'd suggest that there would be an issue making it a through station though, because immediately south you have
The Metropolitan Railway
The Bakerloo Line
The Jubilee Line
The Victoria Line
The Post Office Railway (I think)
All of which have to be avoided.
In addition I don't think anyone would be endeared to digging a big hole in a Royal Park, nor would the owners of the obscenely expensive houses around the area be particularly happy with the extent of required work right at their doorstep (and they're the sort of people with the money to have real political contacts).
My original intent in using that corner of Regents Park was to build a terminal station both for HS2 and to take over the functionality of Euston. Its a location where you could feasibly redirect the incoming lines that currently go to Euston.
Then once Euston station is made vacant you can rebuild it as you wish, a lot faster and more economically.
Then when Euston is re-established the extra platforms in the Regents Park station would give HS2 room to grow.
Now like I said, the original intent was for a terminal station. If it were a through station then it would go deeper but with a fraction of the platforms and with minimal disturbance on the surface (you'd establish a station box and then mine outwards from that).
And also a through station would have a different alignment. Instead of having platforms running more or less north-south, a through station would be more east-west. That would allow an easier path back towards OOC, which would be the actual home station. I wish I could add more but I don't have the path for CrossRail2.
On a similar note, Euston Square Gardens is 200m long. If you were to build a station box there and then run the platforms east-west you could also construct a through station there. It would involve mining under and outwards from the end of the station box but the difficulties in doing so would be manageable.
If you were clever you'd also consider constructing a link between Euston and Kings Cross at the same time (Pedestrian and/or provision for a people mover).
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To be fair the HS2 documents were never very easy to find to start with, and I think some have gone in the move to .gov.uk. However I think the process of optioneering for the London terminus is documented somewhere in the "London to West Midlands and Beyond" report which has now popped up on Railways Archive.
http://www.railwaysarchive.co.uk/do...hor=all&publisher=all&published=all&submit=Go
Thanks muchly
