Cundy said earlier on Monday that due to conditions in the tower, which "verge on indescribable", it could takes weeks to locate bodies and there was a likelihood some of those lost would never be properly identified.
The fire has prompted warnings about fire safety risks in many other council tower blocks built in the same era.
"There's one woman this morning and her child, they have been moved three times since Wednesday into different accommodation".
"It was a very angry crowd". May has announced a fund of about $6.5 million for the victims.
Experts believe the exterior cladding, which contained insulation, helped spread the flames quickly along the outside of the tower in the June 14 blaze.
Community groups have said warnings about poor fire safety have always been ignored, and that in the aftermath of the disaster, officials had failed to immediately take care of those affected.
She also defended the fire service's advice for people to stay in their flats during tower block fires, saying that having everyone evacuate from such blocks through a single staircase would cause further injuries and hamper efforts to put out smaller blazes.
The 23-year-old Alhajali is the only victim of the Grenfell Tower fire to be officially named as the hard process of identifying human remains continues.
A short walk away, however, are apartments and houses that cost millions and are home to a wealthy elite. "We will continue to look at what more needs to be done", Mrs May said in a statement issued by her office.
"Afterwards, she will meet a group of residents, victims, volunteers and community leaders in Number 10".
Neither side immediately released details. "This prime minister is not viable". Residents want answers on why the fire spread so quickly, trapping numerous estimated 600 residents.
Alongside both police and fire investigations into the blaze, she has promised to set up a public inquiry, Reuters news agency reported.
Met police commander Stuart Cundy told a media briefing Friday that 30 people were known to have died, including one person who died in hospital after being rescued.
This will ensure those involved in the response to the tragedy are able "to receive targeted support should they need it", Downing Street said.
Anger flared in the Kensington community over the weekend - with many protests taking place across the capital - as some accused the authorities of withholding information and responding inadequately.