UPDATED 7.01AM: British Prime Minister Theresa May has been rushed away under heavy police guard as protesters shouted "Shame on you" after she met residents who live near a tower block in London where at least 30 people died in a fire.

May, already under pressure after a botched snap election, is facing widespread criticism for her response to the blaze.

She has promised to set up a public inquiry and pledged STG5 million ($A8.9 million) to help the victims.

Separately, hundreds of protesters stormed the local town hall chanting: "We want justice."
May has outlined a series of measures to help those left homeless by the devastating fire which engulfed the 24-storey North Kensington apartment block on Wednesday.

But fury has grown in the local community at what people say is the slow response from authorities to the fire and a failure to inform families and friends about the fate of loved ones.

Media reports have said about 70 people are expected to have been killed, although police have not confirmed this.

Local residents also say they are angry their safety concerns had been ignored and that people had been told to stay in their flats in the event of a fire.

May, who on Thursday met emergency services at the fire site but did not meet locals, visited residents, volunteers and community leaders at a nearby church on Friday and was rushed away afterwards by police as an angry crowd outside shouted "Coward" and "You're not wanted".

Meanwhile, several hundred protesters stormed Kensington and Chelsea council town hall.

The protesters barged their way through an automatic door at and sought to gain entry to an upper floor. Police barred their way and scuffles broke out.

The protesters chanted: "We want justice" and "shame on you". The protesters were angered when no one from the council came out to address their concerns.

The local authority, which owns the tower block where families rent their homes, says it is doing all it can to support the victims and help the relief operation.

The Grenfell Tower, which housed some 600 people in about 120 apartments, is in a low-rent housing estate next to one of the most affluent areas of Britain.

There have been demands for answers as to how the blaze was able to engulf the building, trapping many on the upper floors. Exterior cladding that was added during a recent refurbishment might have played a part.

Earlier on Friday, May met victims privately at a central London hospital.

"I spoke with people who ran from the fire in only the clothes they were wearing," she said in a statement. "They have been left with nothing - no bank cards, no money, no means of caring for their children or relatives."

Even some within her own party said May should have faced the locals herself earlier.

"She should have been there with the residents. You have to be prepared to receive people's emotions, and not be so frightened about people," former Conservative cabinet minister Michael Portillo told the BBC.

Queen Elizabeth, 91, and her grandson Prince William also visited residents and emergency workers on Friday.

"That's one of the most terrible things I have ever seen," William said of the tower's blackened shell.