while that's true, intercity trains in the UK run at 125mph, which I believe falls into the "high speed" category in the U.S.

Also frequency wise the Uk wins over this link. London to Edinburgh, 534km, takes 4h20 and runs every half hour.

HS2 is under construction which is a true high speed line and will knock an hour off trips to Manchester, Glasgow and Edinburgh, and allow more frequent trains (the WCML can only support one train an hour to Glasgow for example as the lines south of Rugby are crammed - over 40tph in each direction, or one every 3 minutes on each track)

HS2 will arrive in 15 years optimistically (20 years realistically) and will only get you from London to Leeds - the other half of the distance to Edinburgh or Glasgow will still be on slow tracks... Better than the US for sure but two decades behind FR, DE, IT or ES.

Sure it's slow, but there will be big savings in 8 years time when London-Crewe opens up.

The UK doesn't really have a great market for long distance trains in the same way that Europe does. If we weren't so insular and joined Schengen, then sure - high speed trains to Paris/Brussels/Cologne/Amsterdam from Birmingham/Manchester/Leeds/Bristol would work, but there's very few trips more than about 200 miles.

HS2 isn't really worthwhile as a speed improvement, the main benefit is the increased capacity -- effectively six-tracking the WCML south of Crewe (and 4 tracking the Crewe-Manchester link).

> intercity trains in the UK run at 125mph, which I believe falls into the "high speed" category in the U.S.

That would definitely be high-speed according to German standards. Local trains top out at 120 km/h (75 mph) or very seldomly 160 km/h (100 mph).