No fewer than 50 people were injured and some residents were trapped inside the towering inferno.
"At this time I am sad to confirm that we now know that there have been fatalities", Cotton said in a statement early on Wednesday.
On Twitter, London Mayor Sadiq Khan said the fire was declared a major incident; he and other city officials are spreading information about how survivors and families can find one another or report someone missing.
"People were still sleeping on the higher floors, they didn't have a clue what was going on, I'm not even sure if half of them got out to be honest with you, there was kids out the window", resident David Benjamin said.
Khan added: "Thankfully residents didn't take that advice but fled. these are some of the questions that have to be answered".
The London Fire Brigade dispatched at least 40 fire engines, 20 ambulance crews and more than 200 firefighters in an effort to battle the conflagration at the 24-story Grenfell Tower in West London. One resident said the fire alarm did not go off - bolstering the arguments of a community group, which only months ago had warned of a potential catastrophe at the subsidized housing block. The fire commissioner said that the cause of the blaze is still unknown.
Photos and video shared on social media show the tower block engulfed in flames.
A residents' action group said its warnings about safety had fallen on "deaf ears".
Other witnesses said the fire spread rapidly up the building, with some suggesting it was fuelled by gas.
Another witness, Tamara, told the BBC she also saw people trying to throw their children to safety.
Nassima Boutrig told The Associated Press reports: "We saw the people screaming", she said. It's gone. It's just a matter of time before this building collapses. Hours after the fire broke out, a plume of smoke can be seen from miles away.
London Fire Brigade Assistant Commissioner Dan Daly said firefighters were "working extremely hard in very difficult conditions to tackle this fire". "The fire started on the upper floors. oh my goodness, it spread so quickly". The police closed the A40, a major road leading out of west London, in both directions.
"I was just screaming at people: "Get out, get out" and they were screaming back at me: "We can't, the corridors are full of smoke", he told BBC Radio.