A market working does not imply the creation of unlimited supply. Governments that restrict building are an external factor. Markets can only operate within those bounds. Since land for building is scarce, prices rise.
There are other factors, of course. Just speculation does not really seem to be a major one.
Key word here being "working". The market is literally hindered here by said government. The natural response to high demand for housing would be more housing and higher density housing. Zoning laws do a fantastic job of hammering that down.
There are other factors, of course. Just speculation does not really seem to be a major one.