I think the housing crisis all over Europe is a major frustration for many people. And yes it is connected to immigration in that demand is simply higher than the supply. Also, everyone wants to live in the center of big citites. The population craves coffee shops, concerts, the freedom that the big cities offer.
I do think that, perhaps a little bit boringly, that great public transport as well as government encouraging construction and development in the cities is one of the best things government can do. It doesn't matter what kind of housing, just more, more, more. The market will take care of the rest.
Of the cities I know, Berlin is by far the best in this regard. You have a fantastic, efficient transportation system. You don't really need a car, and the suburban traffic is incredibly low, considering the size of the city. It has relatively cheap housing, encouraging lots of hard working and creative young to live there. It's a place I would live, if it wasn't for all the germans!
As a counterexample, Lodz, where I live has cheap housing, but bad public transport and horrible traffic. These factors really limit the enjoyment of living here. While Oslo, having decent public transport, has extremely slow, expensive and rigid housing regulation, creating unfathomably high housing costs exceeding London.
High cost of housing also creates the relatively unproductive class of capitalists called Landlords, whose income is more likely to hold more productive citizens down, rather than result in competitive, risk taking, growing businesses. My uncle in Britain is one of those, owning 4-5 houses. The cheapest, greediest bastard I've ever known, who is not interested in creating wealth or developing his properties. Just to safely and surely secure himself a steady income so he could pension himself early.
