Is that really a problem outside of London, SF, and one or two other super-appealing cities? Honest question, I have no idea.
There is also some tax break that if you had no income in Portugal in the last 10 years, you are eligible for a very reduced personal tax rate if you move to Portugal for X years so that also brings up rental and property prices.
Related thought... I wonder how much AirBnB plays into this? I'm vacationing in Florence later this year and was surprised at the large number of available flats in the historic center. Not just rooms, or random apartments, but in some cases significant portions of buildings.