At 8.55am, 125 firefighters and 20 fire engines from Poplar, Millwall, Shadwell, Plaistow, Whitechapel and surrounding fire stations were called to the scene of a fire at New Providence Wharf in east London.
Parts of the eighth, ninth and 10th floors were on fire, the London Fire Brigade said.
The Brigade's 999 Control Officers have taken 13 calls to the fire.
Pictures and videos shared on Twitter showed the blaze several stories high.
A spokesperson for London Fire Brigade tweeted: "Fifteen fire engines and around 100 firefighters have been called to a fire on Fairmont Avenue in Poplar. More information to follow."
The London Ambulance Service are also on the scene.
A spokesperson for LAS tweeted: "We have responded alongside the London Fire Brigade to a fire in a residential building in Poplar.
"A number of crews, including from the Hazardous Area Response Team and The London Ambulance Service Emergency Planning & Resilience Officers are on the scene."
Kenneth Law, a resident opposite the tower block, told the Standard: “I live in the building right across it and I was woken up with the noise of fire engines around just before 9am.
“I only saw smoke coming out from one apartment and the firemen were all on the ground floor. My worry was just whether people were aware and getting out.
“I still see people looking down from apartments to see what’s going on.”
Mr Law said the area around the estate remains blocked off with many fire engines still at the scene.
“ It’s not nice seeing it, it’s so burned out and it’s right in front of me.”
The London Ambulance Service added that they’ve treated a number of people, and “remain at the scene, working with other emergency services.”
Residents at New Providence Wharf have been fighting to remove the building's cladding since the 2017 Grenfell Tower fire that killed 72 people.
It was discovered that New Providence Wharf is fitted with ACM Cladding following a report commissioned by developer Ballymore from Hoare Lea Fire Consultants/ Engineers, according to The New Providence Wharf Leaseholders & Residents Association (NPWLRA).
The building features ACM on approximately 22 per cent of the façade, Ballymore said.
Work to remove the cladding was due to begin in April, developers Barrymore told the East London Advertiser.
“To replace elements of a facade under these circumstances is an extensive process,” Ballymore said in a statement in January.
“We have a project team in place which has already committed months of work to arrive at a workable and cost-effective solution.”
The local Labour MP Apsana Begum said the residents had been “left vulnerable and unsafe” due to fire and building safety defects.
She told the Standard: “For years now, constituents at New Providence Wharf, where there are 1,500 apartments, have been left vulnerable and unsafe due to numerous fire safety and building safety defects and that ACM cladding remains on these buildings.
“The fire this morning shows just how serious this issue is and why constituents have been right to continue to raise alarm bells for so many months. My thoughts are with all my impacted constituents during this incredibly difficult time.
“The developer Ballymore have promised action but to date, constituents have not received information on fire engineer reports and details of any remediation works.”
Ms Begum added that there has been “a failure” to address a series of building safety defects from lack of hot water to broken paving.
“Meanwhile Ballymore recorded profits of £80m through subsidiaries last year and their net asset value is estimated to at more than £500m,” she added.
“It is simply not good enough for developers to say that they cannot act or that they are and then do nothing. They must act now and the government must act now and hold them accountable in order to protect residents.”
In a statement to the Standard, Ballymore said: “Our thoughts are with everyone who has been affected by this morning’s fire at New Providence Wharf. The safety of our residents is paramount and we are working closely with the London Fire Brigade.
“We can confirm that the fire was quickly brought under control by the Fire Brigade and is now extinguished. Our response team are on-site to support residents and assist with alternative accommodation where necessary.
“We will update once we have more information.”
It comes as the Fire Safety Act, which is aimed at making homes safer following the 2017 disaster, passed through parliament last week.
The Government said it has created a £5 billion fund to remove flammable cladding from tall buildings.
But the fund will only cover removing flammable cladding on buildings more than 18m tall, with those in smaller buildings required to take out loans.
The loan scheme will cap costs at £50 a month for safety work on buildings between 11m and 18m high.
Homeowners have said this has left them trapped in unsellable flats due to the cladding crisis, with people planning a summer of protests to combat the costs.
A spokesman for End Our Cladding Scandal, a coalition of homeowners from across the country, said: “We are feeling deflated but we have been here before. We have got a band of Conservative MP supporters now and there will be no end to campaigning.
“We are taking some time to regroup and then plan a rally and protest in the summer.”