A fire that engulfed a London tower block this week killed at least 58 people, police say, as Prime Minister Theresa May admitted the response from the authorities had not been good enough.

With anger mounting over the government's handling of the blaze, May on Saturday met residents from the Grenfell Tower and pledged to support the victims as protesters gathered in the streets around her residence for a second day.

May has been criticised for her muted response to the fire and had to be rushed away from a meeting with residents on Friday under heavy police guard as protesters shouted "Shame on you".

"The response of the emergency services, National Health Service, and the community has been heroic," May said in a statement.

"But, frankly, the support on the ground for families who needed help or basic information in the initial hours after this appalling disaster was not good enough."

London Police Commander Stuart Cundy said the toll of 58 represented those who were missing and presumed dead from a fire which ripped through the 24-storey social housing block as residents slept in the early hours of Wednesday morning.

"Sadly at this time, there are 58 people who we have been told were in Grenfell Tower on the night that are missing and therefore sadly I have to assume that they are dead," he said.

While the blaze has prompted an outpouring of generosity, with many people donating provisions and clothes, it has also unleashed rage at the authorities as the charred tower was cast as a deadly symbol of a deeply divided society.

On Friday angry protesters chanting "We want justice" stormed their way into the Kensington and Chelsea town hall to try to confront the leaders of the local council.

Residents of the destroyed tower said May was far too slow to visit the stricken community, that the building had been unsafe and that officials failed to give enough information and support to those who lost relatives and their homes.

On Saturday May spent over two hours meeting residents from the north Kensington area at her Downing Street residence and chaired a meeting on the government's response to the fire.

She has promised to set up a public inquiry and pledged STG5 million ($A8.4 million) of support, housing guarantees and help with access to bank accounts and cash. Those who lost their homes will be rehoused within three weeks, she said.

On Saturday more than 1000 people gathered near May's Downing Street office to protest against her plan to form a government with the support of a socially conservative Northern Irish party.

One banner showed a drawing of May with the words "Shame" and "Disgrace".

The Queen, having visited residents of the tower on Friday with her grandson William, also led a minute's silence in Buckingham Palace on Saturday.

"It is difficult to escape a very sombre national mood," Elizabeth said in a message on her official birthday. "The country has witnessed a succession of terrible tragedies.

"Put to the test, the United Kingdom has been resolute in the face of adversity," the Queen said.

"United in our sadness, we are equally determined, without fear or favour, to support all those rebuilding lives so horribly affected by injury and loss."