The UK's HS2 is really about freeing up more commuter capacity on the existing lines into London - currently both the express and stopping services use the same line requiring large gaps. By separating the fast and slow trains they'll be able to schedule more trains. If you're going to build a new line might as well make it high speed.
If you've ever been on a London commuter service you'll see they're pretty packed.
I don't think people particularly care about high speed rail in Britain since the vast majority of the population live within 200 miles of London and our existing trains go up to 125mph on the mainlines so get you to London in a couple of hours or so.
Edinburgh or Glasgow to London is a similar distance as LA to SF. Those trains take about 4 hours right now versus 8 hours on Amtrak, about the same as the 8 1/2 hours the Flying Scotsman took from Edinburgh to London in 1888.
If you've ever been on a London commuter service you'll see they're pretty packed.