He said the number of confirmed fatalities in Wednesday’s inferno remains at 30.

Cundy said 16 bodies had so far been recovered from the tower and taken to a mortuary.

Police do not expect to find any survivors inside the 24-storey concrete tower, which contained 120 flats.

On the figure of 58, he said: “I really hope it won’t, but it may increase,” and “it might be that some of those are safe and well” but for some reason had not yet made themselves known to the police.

“Our focus has been on those that we know were in Grenfell Tower. However, there may be other people who were in there on the night that others were not aware were there,” he said.

“That is also an absolute priority for the investigation – to establish who they may be,” he added.

Cundy said police had now managed to get to the top of the tower and had undertaken a first visual search for victims, ahead of later painstaking searches.

“There is considerable damage within Grenfell Tower,” he said.

“We have colleagues in there as we speak, searching for and recovering those that have died.”

Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people “if there is evidence”.

“We investigate criminal matters. The investigation will identify any criminal offence that has been committed,” he said. “It will go to establish the answers of what happened in the fire and how it spread; it will look at the building itself; it will look at the refurbishment as well ... Our criminal investigation will identify any criminal offences that have been committed. Wherever we can, we will bring people to justice if there is evidence.”