A man aged 54 suffering burns was taken to a south London hospital where his condition is understood to be critical after the fire in Streatham.
Police inquiries are underway after two bodies were found at the scene of the fire, on waste ground at Streatham High Road SW16, near the junction with Lewin Road.
Police were called to the scene at around 2.30am this morning.
London Fire Brigade extinguished the fire.
The Met say post-mortems will be scheduled in due course.
More top news
Hackney actor Idris Elba and Croydon rapper Stormzy donned Santa outfits and paid Newham and Whipps Cross children's wards a visit.
James Scobie QC represented Tokyi Ajibola, otherwise known as Trapstar Toxic, in his trial over an alleged gang-related shooting.
The memorial will focus on remembering the 71 victims of the tower block fire.