The argument of the empty apartments in Berlin comes up all the time, but it is a myth. Maybe in London it is different, for various reasons, but in Berlin, that is not the reason for the issues. [1]
Even if only new luxury apartments are being built, it is more housing that takes pressure off the market. The wealthy people can move into those apartments, freeing their old less luxurious apartments for "poorer" people.
And there is no "free market" for housing here - it is very difficult to build, with lots of regulations.
And who wants to invest, when the government will seize your assets as soon as you are successful? Last year they introduced a hard cap on rents, that applied no matter how much you paid for the house you wanted to rent out, and no matter where it was located.
In two weeks, there will be a public vote to seize thousands of flats at "way below market value" (quote from the voting sheet) from corporate landlords. These are not conditions where a "free market" can do its thing.
As a matter of fact, only big companies have the means to build under such conditions, it is much too risky for smaller entities.
But then, sure, blame the evil capitalists for the issues your socialist government has created.
[1] https://www.tagesspiegel.de/berlin/wohnungsnot-leerstand-in-...