Madeleine's parents feel the latest development is "potentially very significant", the family's spokesman says.
Rough sleepers given emergency accommodation could be evicted within weeks, a charity says.
More than half the population has struggled with sleep during the lockdown, especially younger people.
It comes as UK police chiefs say they stand alongside all those "appalled and horrified" by the death.
Business Secretary Alok Sharma is tested for coronavirus after feeling unwell during a debate.