Ticket prices in Britain aren’t due to privatisation. They were a side-effect of the unexpected success of British Rail in its final years at attracting more passengers. As demand went up, the ailing infrastructure struggled to cope. Upgrades can take decades to plan and execute correctly, so the answer was to raise prices to ease off demand.
This also fulfilled the longstanding policy of both parties for rail users to carry the financial burden of rail operation and maintenance. So, under privatisation, 40% of tickets were priced directly by the Department for Transport. The rest were priced by the train operators, who often engaged in price wars that lowered prices compared to the controlled fares.
Now of course privatisation is effectively over and 100% of tickets are priced by government. Prices will still be maintained high because of the desire to make passengers pay for the system, and to keep demand manageable. Already some routes have reached saturation.
Pity SpaceX doesn’t believe it has to obey the law, and thinks it can just buy land and dump waste on it.