In a statement issued after the visit, Mrs May said: "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".
British Prime Minister Theresa May promised victims of a London fire that left at least 30 dead that a five-million-pound ($6.5 million) support package would be created, the media reported. And as NPR's Frank Langfitt in London, police are hoping that the death toll will not reach the triple digits.
"This number 58 may change".
Cundy said the images and video of the scenes inside the Grenfell Tower would be released on Sunday, adding "We will not do that until we have contacted all the families we are supporting to let them know that's our intention".
More than 70 people reportedly remain unaccounted for and the area surrounding the tower has been plastered by distraught relatives with pictures of the missing, from grandparents to young children.
A firefighter who climbed to the 15th floor as the Grenfell Tower was ravaged by flames feared the block would collapse like the World Trade Centre.
May announced on Friday that her government has set up a £5 million ($8.4 million Cdn) "discretionary fund" to help pay for food, clothing, personal supplies and funerals.
"It is hard to escape a very somber national mood", Elizabeth said in a message on her official birthday.
Meanwhile, dozens of people erupted into Kensington and Chelsea town hall to protest the lack of response following the fire.More news: Oil prices under pressure on worries data will confirm rising US stockpiles
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".
It came after she met victims of the blaze at Downing Street, amid criticism she had not seen them in the immediate wake of the disaster.
"Our focus has been on those that we know were in Grenfell Tower".
There are 16 bodies now in a London morgue, Cundy said, and the remaining victims are missing and presumed dead. "As soon as we can, we will locate and recover loved ones", he said.
Sixteen "very ordinary people" sat in Downing Street to bring their concerns to May in an "unprecedented" meeting on Saturday and finally felt they were listened to, the Bishop of Kensington, Dr Graham Tomlin said. "I absolutely get why they are angry".
Commander Cundy said the police investigation into the fire "will take weeks, it may take longer than that".
"We entirely support the calling of the public inquiry and will co-operate in whatever way we can with it so that local people have all the answers about what has happened", the council said.
However, even those within her own party said Mrs May should have faced locals herself.
Queen Elizabeth II marked her official birthday today by saying Britain remains "resolute in the face of adversity" after the horrendous fire and recent extremist attacks in London and Manchester.