More than 200 firefighters were needed to bring the blaze under control at the six-storey Spectrum Building in Dagenham.
The building was shrouded in scaffolding to allow remedial work to the top two floors where non-compliant cladding was being replaced.
Matt Wrack, Fire Brigades Union general secretary, said: “Once again, a fire has erupted in a residential building wrapped in flammable cladding. There needs to be an urgent and swift investigation of how this has been allowed to happen.”
London Fire Commissioner Andy Roe said: “The building has a number of fire safety issues known to London Fire Brigade.
“We will now begin a full investigation into the fire and its cause. This was a very dynamic and challenging incident, and we know there will undoubtedly be concerns around the fire safety issues present within the building and this will form part of our report.”
More than 80 people were safely evacuated from the building with two taken to hospital.
The Dagenham blaze came a week before the final report is published of the official Grenfell Tower Inquiry into the tragedy in June 2017.