The plan for HS1 - HS2 was to piggyback off the provision for a spur just west of where HS1 leaves the tunnel at Kings Cross.
Don't think it was designed for high speed, just linking the two routes just outside the termini. See link for the route plan (on 4 sheets). The HS2 junctions would be in underground (step plate style) junctions.
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HS2 plan and profile maps: HS1 - HS2 link
These are the plan and profile maps for Phase One of HS2 between London and the West Midlands.www.gov.uk
For those that don’t know, the proposal was to take over the existing westbound track of the North London Line between the link to HS1 and Primrose Hill station. The North London Line services would be diverted onto reinstated tracks to the north around Camden Road station, but (and as “buts” go its a biggy) between Camden Junction and the WCML it would take the existing line. The impact on freight and the London Overground services would have been considerable.