"We need to know what commitment the council is taking to ensure this tragedy is not repeated", he said.
Cundy said one of the victims was a person who died in hospital.
Police and fire experts have said the fire was so intense that the process of identifying human remains will take weeks, if not months - and some victims may never be found. Police say at least 58 people are either confirmed or presumed dead, with the figure likely to rise in coming days.
Grenfell Tower is part of a social housing estate in north Kensington, just streets away from some of the most expensive homes in the world in Notting Hill.
As the protesters sought to gain entry to an upper floor, police tried to bar their way.
The government has ordered a judge-led inquiry into the disaster, which is under pressure to act quickly.
Speaking to the cameras, he praised the local community spirit, to which one woman shouted: "We can't say the same for the authorities".
Pence hires outside legal counsel
Attorney for the Eastern District of Virginia Richard Cullen , who is chairman of McGuire Woods, the Post reported . But obstruction came into play after Trump fired Federal Bureau of Investigation director James Comey last month.
She met with injured survivors in hospital on Friday, visiting Chelsea and Westminster Hospital, which is treating eight people.
The announcement comes as the government is accused of failing to improve fire safety in buildings, like Grenfell Tower, despite warnings.
"It's because of the fire and smoke spread".
A fire safety expert said that the blaze was "entirely avoidable".
Yesterday, the first victim of the fire was named as 23- year-old Syrian refugee Mohammed Alhajali.
For resident Soran Karimi, 31, who lives in the block opposite, it was nothing short of "murder" and "people should be prosecuted for this".
The focus of criticism centres on the cladding fitted to external walls on the 1970s concrete block as part of a £8.7 million ($11 million, 9.9 million euros) refit completed a year ago.
The residents of Grenfell Tower have continued to express their anger that nothing was done about the fire risks in the building, despite various complaints they submitted with the council and the fire brigade.
Her government is trying to make up ground in reacting to a fire that trapped people in their beds in the early hours of Wednesday, with many unable to escape as the flames raced up the building, cutting off exit routes and forcing some to jump.
It is believed that contractors chose the cheaper, more combustible version for Grenfell, which has a polyethylene core and is known as PE.