Snark aside, cle has already mentioned that it would be the Primrose Hill route. If you separated the Primrose Hill amd Kentish Town routes at Camden Road (see below), then all of your NLL worries disappear and you only have the freights to the WCML to deal with. One or two trains per hour (max) could deal with that.
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The Skouse lot might find it a bit far on the train, but the Brummie lot (3 times more of them and half the distance from London) might not. From Birmingham, Brussels would be less than 3 hours and Paris about 3.5 hours. Amsterdam and Cologne would be about 4.5-5 hours, but most of the passengers wouldn't be making the full trip. Passengers would alight and be replaced at London and Brussels.
And that's before Old Oak Common adds a potential market from the GWR. A single change at OOC would sound much better for the Thames Valley lot than schlepping up to St Pancras.
So what rolling stock are these trains going to use? 374s UIC GC are currently limited to HS1 and platforms 3 and 4 at Ashford International in the UK. Are the Eurobrums going to be UIC GC and limited to a special International Platform at Curzon street? Obviously the North London Line rebuild for 1 through train a day needs to take this in to consideration. Or are we going to specify a common Euro-Northernmonkey set that will be classic compatible and allow through running to places such as Liverpool?