I take the Eurostar a few times a year for work between Amsterdam and Paris and there's literally no security whatsoever. If there's security to board the Eurostar in routes to/from the UK maybe it's because of Brexit?
I had read some reviews saying Eurostar security was airport like on all routes, but maybe I was just reading some other schmuck's experience on an international route like mine :-). Hopefully anyone reading my comment reads a little farther so they are better informed.
And so, I amend my previous comment. I'd be satisfied with an LNER equivalent, but if I can get Eurostar speeds at LNER convenience, I definitely want that!
I wonder how much the UK paid for the LNER lines, e.g. from King's Cross up to Waverley Station in Edinburgh. Not that it has any bearing on US costs, but I'm curious. Here everything is just stupidly expensive to build, and pretty much any stakeholder can derail the whole thing, even the tiny ones. I'm not a big fan of using eminent domain but there are times when it is the sensible choice.
It's hard to come up with a definite single figure, because you'd have to go all the way back to the original railways in the 19th century and trace your way through all the upgrades that happened bit by bit since then, plus figure out how to handle inflation/purchasing power etc. across such a long time span.
UK to Europe will have border control, passports, etc.
But re: UK<->mainland I guess it shouldn't be surprising that there's more security for the Chunnel crossing. That feels like it would be a much more likely terrorist target than a random HSR route on land.
A few years back Thalys merged with Eurostar and then last year they started rebranding the former Thalys services as Eurostar, too, which probably explains the confusion.
Only the former Eurostar services (nowadays "Eurostar Blue") have the security theatre on account of the Channel Tunnel plus UK being non-Schengen, whereas the former Thalys services ("Eurostar Red") are regular train services just like in the rest of Europe (except for Spain, which does some security theatre for its high speed trains, too, although AFAIK a bit less intense than Eurostar, which in turn is less intense than flying).