Two men were hospitalised after Friday's blaze in Poplar while a further 38 others were treated at the scene.
UK advocacy groups have raised fresh concerns about building cladding after a fire broke out at an east London tower block.
Firefighters were called to tackle a blaze at a 19-storey residential building in Poplar, which had spread to three floors.
London Fire Brigade said about 125 firefighters attended the scene on Friday in the city’s Docklands and brought the blaze under control after several hours.
"Firefighters wearing breathing apparatus have carried out multiple rescues," the authorities said in a statement.
Two men were taken to hospital after suffering smoke inhalation. At least 38 other people, including four children, were treated at the scene by London Ambulance crews for shock and other symptoms.
The property developer that owns the building, Ballymore, said the blaze was "quickly brought under control."
Ballymore has said 22% of the building’s facade is covered in aluminum composite cladding, a similar cladding that contributed to the deadly 2017 fire at Grenfell Tower.
Investigators found that the flammable cladding had accelerated the spread of the blaze at the west London tower block, where 72 people were killed.
Survivors and relatives of the Grenfell United advocacy group said in a statement they were "horrified" by Friday's fire at Poplar.
"When will the government take this scandal seriously? Enough is enough," the group tweeted.
"The Government promised to remove dangerous cladding by June 2020 it has completely failed its own target and every day that goes by lives are at risk."
"We've said all along that another tragedy is waiting to happen unless this crisis is dealt with properly and swiftly."
The Grenfell Tower fire in June 2017 is the UK's worst domestic fire since the Second World War.
Safety regulations brought in since the deadly fire require similar dangerous cladding to be removed, but the work has not been carried out on some apartment towers because of a dispute over who should pay.
In February, the government said they would finance the removal and replacement of cladding for all leaseholders in high-rise residential buildings in England above six storeys or 18 metres high.
Leaseholders in buildings lower than 18 metres would have to pay to replace the cladding, with some loans offered.
But the leader of the UK Liberal Democrats, Ed Davey, has described the delay in action as a "national scandal".
On Friday, Twitter users shared the hashtag #EndOurCladdingScandal to voice their frustrations that many UK buildings still had flammable cladding.
The mayor of London Sadiq Khan said his thoughts were with "all those affected" by the Poplar fire, as he seeks re-election in the UK capital city.
"It is vital that [the] government, developers, building owners, and local and regional authorities work together to urgently remove the cladding from every affected building," he said in a statement.