That was because these were classed as new-builds, which were exempt from the restrictions.
Researchers found that between 1994 and 2010 people in rent-controlled properties paid about $2.9bn (£2.3bn) less in rent.
But they also found that renters who came to the city later paid an extra $2.9bn over the same period, largely because of a shortage of housing.
What could happen in the UK?
Mr Khan wants to set up a register of landlords and rents. And a new London Private Rent Commission would design a system of rent control and set out how rents could be reduced.
At the moment, he does not have the power to do so.
In Scotland, more than 12,000 people recently signed a petition calling on the Scottish government to introduce “proper rent controls”. Petition founder Emma Saunders hopes caps on how much landlords can charge will be introduced.