Prices and rents are left to "the market", but construction is not at all. Strong rent control should be introduced everywhere and ownership for investment reasons should be massively discouraged (e.g. by strong taxation). On the other hand protection of existing landlords should be reduced to encourage new building. Rent seeking is damaging the economy and the society and only privileged landlords benefit from current conditions.
Unfortunately most economists seem to be biased or are probably benefitting themselves, thus there is no concentrated effort to push for better policies.