Five people have been formally identified after a blaze tore through the residential block last Wednesday in west London, Metropolitan Police Commander Stuart Cundy said on Monday.
The rest are missing presumed dead and Mr Cundy said "the awful reality is that we may not be able to identify all those that died" inside what is now a blackened and charred shell.
There were emotional scenes at the site in north Kensington at 11am as firefighters halted work to join residents for a minute's silence held to remember those who lost their lives and all others affected by the blaze.
The silence was also observed at Government buildings across the country.
Mr Cundy said the death toll may still change, but not as significantly as it has in recent days.
He fought back tears as he told reporters at New Scotland Yard about the scene inside the 24-storey tower.
Footage from inside the gutted building has been released, showing the extent of the damage caused by the blaze.
He said it had been "incredibly emotional working in there", adding: "On Saturday I went in myself and went to the top floor.
"And it is incredibly hard to describe the devastation in some parts of that building."
Speaking later outside Scotland Yard, Mr Cundy added: "I have investigated major crime for most of my service and I have seen some terrible things. But I don't think anything prepared me for what I was going to see when I was in there.
"It's hard to describe my feelings, because I cannot imagine, and I would not want to put myself in the position of those families who have lost their loved ones.
"But being with colleagues from the London Fire Brigade when I was in there, colleagues from the London Ambulance Service and other police officers, I think it's fair to say it is incredibly emotional working in there.
"But we will do it with our utmost professionalism and we will do everything we can as quickly as we can to locate everybody who is in there."
Five people who had been reported missing after the disaster have been found safe and well, he added.
Amid anger in the wake of the disaster, which was described by London Mayor Sadiq Khan as a "preventable accident", the Government announced those left homeless will be given at least Â£5,500 from an emergency fund.
Residents will be given Â£500 in cash followed by a bank payment for the rest from Monday and the money will come from the Â£5 million fund announced by Theresa May on Friday.
Mr Cundy said police had received some 70 pictures and videos of the fire from the public and urged them to send more as officers investigate the blaze.
He would not be drawn on the specifics of the criminal investigation of the fire, including whether anyone had been arrested or raids carried out.
He said that a team of some 250 investigators were now working on the case, with a primary aim being to identify victims and inform their loved ones as soon as possible.