Building in the UK is also hard. England, which is like 90% of the population, is very densely inhabited. Cities are sprawling, their road and transit infrastructure barely support their current size, never mind bigger population. Plus, with the housing bubble, people who barely could afford their homes in the first place feel understandably terrified of anything that drops these prices down.
What the UK did post-WWII and is proposing to do now feels quite bold, but also smart: build new cities. Milton Keynes, for example, was built from scratch. In fact Bletchley, of Bletchley Park fame and now a small suburb, used to be the train stop.
It was built from scratch with adequate infrastructure, parks, high and low density zones, schools and fire stations, on land which I can only imagine was much cheaper than the equivalent in London zone 7. It hugged an existing train line so was connected to the rest of the country "for free".
Is that a way forward? Bootstrapping whole towns, instead of trying to keep fighting market forces to squeeze more people into existing towns.
I'm not saying you force people to live there, or displace the homeless there. No, simply provide a cheaper decent place to live, and people will come.