Some witnesses have claimed Grenfell-style cladding was responsible for the ferocity of the blaze.
The fire brigade has confirmed the building did have cladding but not the same type on the doomed tower block where 72 people died in 2017.
Mr Burnham told Sky News: "It does not have the ACM cladding which is now banned, but it does have a type of cladding which does cause concern.
"There will be many people living in buildings with this cladding today who will be very worried."
The Fire Brigades Union has now called for a complete overhaul of UK fire safety after the flames spread "extremely rapidly" through the building.
Cladding fears
Matt Wrack, FBU general secretary, said: "This terrible fire highlights the complete failure of the UK's fire safety system.
"It's deeply troubling to see fire spread rapidly up a building's exterior again - a shocking indictment of the government's shameful inaction after Grenfell. This is not how any building should react to a fire in the 21st century, let alone a building in which people live.
"We need to end the deregulation agenda and the disastrous cuts to our fire and rescue service. It's time for a complete overhaul of UK fire safety before it's too late."
Greater Manchester Fire and Rescue Service firefighters are still working to extinguish the final pockets of the blaze but it is now under control.
Yellow Vest protesters were doused with water during clashes with police and rioting in downtown Paris, ahead of the first anniversary of their nationwide anti-government demonstrations.More from RT:
The Place d'Italie circle in the city's 13th arrondissement descended into chaos as protesters erected makeshift barricades and threw stones at police officers, which responded with tear gas and water cannon.
The protesters overturned several parked cars and set vehicles on fire. A group of Yellow Vests attempted to block a fire truck from getting through to the barricades, which were also set ablaze.
At least in this video, that doesn't appear to be the case - the protesters move the barricades:
A shopping mall and several bus stops were vandalized when the protesters vented their anger over what they deem as government inaction towards their demands, made throughout a full year of weekly demonstrations.
The windows of a bank were smashed during the rioting. The protester groups on social media had earlier called on their colleagues to occupy and block several stores, including the Ikea and Apple stores.
Police were also called in to disperse protesters who were blocking traffic along the Boulevard Peripherique, the city's main ring 'beltway' road.
The authorities revoked their permit to stage a rally at the Place d'Italie, after the protests turned violent. Police had arrested 61 protesters by 3pm, Prefect of Paris Didier Lallement confirmed, adding that some officers were injured in the clashes.
Police fired tear gas as Yellow Vest protesters blocked a major road and erected barricades in Paris, marking one year since the nationwide demonstration movement began sweeping the country.
Clashes broke out at Place d'Italie downtown and near Porte de Champerret on the city's outskirts.
The protesters have also blocked traffic down the Boulevard Peripherique, the main ring road circling the capital. Riot police were deployed to disperse them.
A total of 41 people were arrested on the streets of Paris, police said.
More than 270 protest events were planned to take place across France over the weekend. Thousands are expected to rally in Paris alone, celebrating a full year since the inception of the Yellow Vest movement last November.
The protesters are determined to show that the movement is "far from being dead" and called for a "grand national mobilization," according to one group on social media.
Police, meanwhile, beefed up security in the capital. Local media reported that officers are on the lookout for hundreds of "yellow ultras and ultra-left militants."
The Yellow Vest protests started as a grassroots campaign against government plans to hike fuel taxes. The hikes were scrapped after several weeks of protests but the rallies continued. They grew to encompass other demands, such as better living standards, government accountability, the fight against corruption and for more direct-ballot initiatives. Demonstrators have also demanded the resignation of President Emmanuel Macron.
Some of the Yellow Vest rallies remained peaceful and maintained a cheerful atmosphere. Others have spiraled into fierce clashes with police, widespread riots and vandalism.
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