The UK does have enough land to build. For example, it's estimated that there are enough small areas of land in London within 800m of a tube station to house a million people. These pieces of land are currently "wasteland" with no public access. They're not sites of any beauty.
There are also thousands of empty dwellings which have been bought as an investment.
The barriers to building are complex. For example, landowners often get planning permission to build, which causes the value of the land to rocket. Sometimes it can be worth ten times more overnight. However, instead of investing in building, that land is then used as a trading commodity. Investors make a profit on the land without actually doing anything with it. There is an area of land not far from where I live, which has had planning permission to build up to 50,000 new dwellings. The original farmer now lives abroad somewhere and the profit he made from selling the land to a developer is in a tax haven and the details can't be accessed. Meanwhile, no dwellings have been built, although they're desperately needed. It really is like a real life version of Monopoly.
There are many other barriers, such as the inability of local councils to build social housing, even if they want to. Meanwhile, they're still being forced to sell off high value council housing at a discount, but can't re-invest the money in new housing.
New housing often means new communities need to be developed, but that requires planned infrastructure. It happened after WW2 and could happen again, but there's reluctance by central government to invest and, very often, local NIMBYism.
Additionally, there are issues with interest rates and local incomes.
All in all, leaving housing to the market is failing to deliver the housing which is needed and central government needs to intervene. However, it's unlikely to do that, unless votes are involved and there's a risk of upsetting people who are doing very nicely from a scarcity of housing.