I think the single line is sufficient for the level of traffic.
Trains from Birmingham to Paris would be 3 per day maximum.
Ashford to OOC and Birmingham, or indeed onto GWML to Heathrow or the West, 1tph each way? And freight of course, but running at off hours.
That should be fine for a single line. The trains are all very long though, and running at slow speeds would take up more capacity.
Actually quite a squeeze on a single track all the way from Camden to Old Oak. In a busy area a link configured in this way can quickly become a source of delay. Although trains can be timetabled to miss each other on the single line, if one is running late, the next in the other direction may have to wait single line clearance before the junction on a busy main line, perhaps delaying following trains.
My main issue is the impact is has on the NLL/Overground, and future growth there and at Camden Road itself.
If one track at Camden Road became dedicated to HS1/2 transfer then the entire LO and freight traffic load would have to fit on the remaining single track through the junction, an impossible feat forcing a look at options to widen the bridge, share both tracks in some way or look at more radical alternatives.
I thought of an alternative that diverts the NLL via a short stretch of the MML through Kentish Town, obtaining better interchange with Thameslink and LUL Northern Line as well as a diverted Gospel Oak Barking service.
This Kentish Town idea could also offer another northern branch to absorb some Thameslink inner suburban services, running thence limited stop over the NLL (8 - car trains avoiding short platforms) to join diverted Watford DC lines at Willesden.
http://www.townend.me/files/kentishtown.pdf
With LUL Overground passenger services removed entirely from Camden Road, the 2 tracks through the bridge constraint could be shared flexibly between freight and HS transfer traffic, and the work to improve loading gauge clearance would not face the difficulty catering for UK high platforms that the wider HS only and other continental rolling stock cannot pass.
At the Camden Junction end the connector could join the WCML slow lines via a grade separated junction for freight traffic, with the tunnel continuation to Old Oak Common commencing at a portal near Primrose Hill.
http://www.townend.me/files/camdenjn.pdf
Note I've shown a double track portal for the Old Oak connection, although a single track would also be compatible with these junction arrangement if the separate single tunnel proposal for the connector is retained. Preferably, underground junctions near Camden would join the 2 tracks each from the Euston and HS1 lines into a shared 3 track system to Old Oak and HS2, a much more robust and flexible configuration.