British Prime Minister Theresa May says there will be a public inquiry into the cause of the fire in London that has left at least 17 people dead and around 600 homeless.

Local residents hang a banner over a balcony following the fire which destroyed the Grenfell Tower block, in north Kensington, West London, Britain June 15, 2017.  [Photo/Agencies]

The judge-led inquiry will also ask what lessons can be learned from Wednesday's fire at Grenfell Tower, and what the tragedy means for the safety of the United Kingdom's 4,000 residential high-rises.

May visited the scene of the fire on Thursday but angered many people by not meeting those affected by the fire. Labour leader Jeremy Corbyn also arrived at the scene and met victims, telling them he will represent them.

"There is desperate stress and sadness," he told reporters. "There are still bodies to find in that dreadful building. We will demand and get answers."

Firefighters, meanwhile, will search the charred shell of the building for bodies. Dozens of people are missing, including members of three families who lived on the upper floors.The search and rescue teams will use sniffer dogs, and build internal shoring as they go.

Firefighters have been to all 24 floors but have not been able to conduct a thorough search because of the fragility of the building. The fire commissioner estimated that the search for bodies could take weeks.

The fire began at 12:54 am on Wednesday and was not fully under control until more than 24 hours later. Commentators have speculated about the role of external cladding in the spread of the blaze but the cause of the fire and what allowed it to accelerate are not yet known.

As of Thursday afternoon, more than 30 people were still being treated in hospital. Seventeen of those were described as being in critical condition.

The queen issued a statement offering her sympathy to those affected by the fire.

"My thoughts and prayers are with those families who have lost loved ones in the Grenfell Tower fire and the many people who are still critically ill in hospital," she said.

Meanwhile, criticism of the management of Grenfell Tower has been growing. David Lammy, the member of Parliament for the Tottenham area of North London, who may have lost a family friend in the fire, was especially critical.

"This is the richest borough in our country treating its citizens in this way and we should call it what it is," he said. "It is corporate manslaughter. That's what it is. And there should be arrests made, frankly. It is an outrage.

"Those 70s buildings, many of them should be demolished. They have not got easy fire escapes. They have got no sprinklers. It is totally, totally unacceptable in Britain that this is allowed to happen and that people lose their lives in this way."