Paul Woodrow, head of operations for the London Ambulance Service, said 20 of the injured were in a critical condition.
"I spoke to one of my officers who was very near when someone came out the window, and he was in tears and he is a professional fire officer, " Ms Cotton told Sky News.
The group claimed access to the building was "severely restricted" for emergency services and other vehicles and that residents were advised to stay in their flats in case of fire. Children and a baby were seen being thrown out of the windows to be caught by emergency workers and members of the public below.
Pictures were quickly circulated on social media.
Prime Minister Theresa May promised an investigation and visited the site on Thursday.
Labour leader Jeremy Corbyn has toured the area near the west London tower block devastated by a fire, meeting with volunteers helping victims and promising to get to the bottom of what happened.
The tower block was recently refurbished at a cost of £8.6m (€9.7m), with work completed in May a year ago. Fire Commissioner Dany Cotton says specialist dogs would start searching the 24-story building.
Rydon, the firm responsible for the refit, said the project "met all required building regulations".
Survivors told of frantic attempts to escape during the fire.
Thursday morning, smoke was still wafting out of the shell of the Grenfell Tower.
About 16 hours after the fire started, pockets of flame were still burning inside and fire crews had managed to reached the top.
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Aujourd'hui s'ouvrent les épreuves du baccalauréat , sacro saint diplôme des études secondaires, souvent décrié mais toujours là. En 2016, 92.3% des candidats côte-d'oriens au bac général avaient été reçus, juste derrière ceux de Saône-et-Loire (92.5%).
He said that number was expected to rise and firefighters have said they did not expect to find any more survivors after rescuing 65. Some jumped to their deaths rather than face the flames, and witnesses reported seeing small children thrown from the tower by their families in a desperate bid to survive.
The fire triggered a wave of mourning in a country already battered by a string of terror attacks. "My thoughts are with local community".
Volunteers in the city of Glasgow - 550 kilometres (350 miles) away - sent a truck laden with nappies and other supplies.
Queen Elizabeth II praised their bravery and their commissioner noted the trauma they had seen.
An eyewitness of the event said Adele was "offering her support to everyone affected by the tragedy".
A 12-year-old is still reportedly missing.
But Kostas Tsavdaridis, associate professor of Structural Engineering at the University of Leeds warned: "Some materials used in facades act as significant fire loads".
The instructions were presumably given so firefighters could be identified if they perished in the fire.
Artist Khadija Saye, 24, who is now showing her artwork in the Venice Biennale, was in her flat on the 20th floor, with her mother Mary Mendy, who is thought to be in her 50s.
She told the MailOnline: "Jessica called me".
Up to 600 people lived in the 120 apartments at Grenfell Tower.
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