Did rents surge during past times of stagflation?
In some cities you get time-sharing beds. In 2003 I lived (for 3 weeks) in a house in London, I had my own room - the largest in the house. A smaller room had a couple with a baby, the loft had 3 mattresses in it but 4 people living there, time-sharing with the mattresses like you have in a nuclear submarine.
There's plenty of opportunity for landlords to increases costs even if peoples incomes can't support an increase.