Really that won't help. These kind of regulations have been tried in so many countries before and the result is always the same: cap the rents => landlords will take houses from the markets and sell them instead => there will be a shortage of properties for rent so finding them will be very hard, and the few landlords left will be extremely selective when choosing from the many candidates.
What does help: increase the supply. Make it easier to build or let houses by reducing bureaucracy, invest in housing projects etc.