The Red Tape Challenge is currently focusing on Housing and Construction. The Challenge shifts its spotlight periodically, though more than one area is looked at concurrently.
The Housing and Construction Challenge says it will last five weeks, although there is the minor technicality that it doesn't tell you when the five weeks started (doh!). However that information can be found on the "All themes" page: the Challenge started on the 12th January and ends on the 16th February.
Within Housing and Construction there are four sub-themes, one of which is Private Rented Sector (no mention of privately-owned housing generally eg owner-occupation). On the left of the screen you'll see a list of all the relevant secondary legislation which in this case includes EDMO regulations, HMO regulations and so on. As far as we are aware the focus of these Challenges is on secondary legislation rather than primary legislation ie quick wins.
The Housing and Construction Challenge page is here.