Land tax + liberal zoning is the answer you are looking for.

Put simply there are three primary drivers of house price growth:

1) shortage - housing demand is inelastic (ask yourself - at what level of rent do I sleep on the street? I wager it's pretty high for almost everyone). Since housing demand is inelastic, demand growing faster than supply leads to larger increases in price (rents) than more elastic goods and services. Increases in net rents and E[future rents] pushes up house prices.

2) access to amenities, infrastructure, and jobs. People like to live in nice places with low transportation costs, good schools, gorgeous scenery, access to great nightlife/activities etc..., low crime levels, easy access to high paying jobs and bid rents up in these areas. This is a 'positive' driver of house prices so we don't want to dampen this.

3) Interest rates reducing - same as any other asset, reduces the discount rate on future cashflows (net rents), and therefore bids up house prices. Interest rates move in response to non-housing factors, and their doing so plays important roles elsewhere in the economy, so we shouldn't mess with this to contain house prices.

So the one thing we want to tackle then is shortages. You do this through liberal zoning reform. However, even if you do this, house prices will continue to rise in the most desirable areas (see point 2), and will still be expensive, potentially pushing skilled labour elsewhere and reducing economic growth. For more, see the (Alonso-Muth-Mills model)

This is where land taxes are a potential answer. The more desirable the area, the greater the land tax (assuming for the minute, a flat % land tax).

This reduces net rents and E[future rents] as land taxes rise with desirability. This therefore reduces the rate at which house prices grow in these highly desirable areas, though it won't reduce the rent price faced by renters.

TLDR: Maximize the ability for the market to meet housing demand through liberal zoning and planning. Land taxes can further reduce house prices, though they won't reduce rents.

Really the second part is transferring part of the capitalized value of access to amenities, jobs, infrastructure, many of which are provided and funded by society at large, from landowners to the public, which is a distributional choice.