Also in London we dont have space to build massive carparks everywhere so lots of people in London dont have cars.
I'm not sure that's true for HS2. In practice the UK builds occasional new roads and very rarely new rail. Crossrail and Thameslink are exceptions that took decades to get approved.
I'm guessing even a busy/congested freeway has a greater throughput per lane than transit; even with automobiles with only 1-2 people in it, vs a train that may have hundreds but pass only every few minutes at most.
One problem with roads is that once you get off the freeway, you need more roads to serve housing and businesses; and the size of those leaf nodes pushes businesses and houses all further apart from each other, necessitating MORE road trips and decreasing walkability.
Not even remotely close: https://en.m.wikipedia.org/wiki/Route_capacity
https://www.fhwa.dot.gov/policy/23cpr/appendixa.cfm (scroll down a little ways)
so your reference for freeway is likely using a single lane number not the actual cost of a 4 lane high way which would be 12 - 80 million per mile.
I wish I knew how much that cost, but I'm starting to see its point now.
Guided busways exist, but as far as I know nobody's doing platooning yet? Edinburgh had a guided busway for a few years but eventually built a tram over it because buses couldn't manage the throughput.
Heavy rail; 50 million
Light rail: 25 million
Freeway:5-10 million
So why aren't they simply doing dedicated roads for transport?
With AI platooning and supervised self driving, "trains" of busses can run along those lines, but split off and merge in from local service seamlessly.
Commercial traffic (even through traffic) can piggyback on low traffic periods.
In emergencies, they are additional roads for evac or supply.
Roads are much more easily repaired and fail less catastrophically.
Electrification of busses is well underway and should be simpler / cheaper for recharging infrastructure.
Platooned "trains" of busses will conserve energy and likely could go 100 mph or more with proper convergent sensors monitoring and maintenance.
Safety should be equivalent.
I suspect there are political nuances where rail gets its own budget apart from roads, whereas dedicated roads get thrown it with general road funding, and then wouldn't get proper funding.