We will continue to look at what more needs to be done.
She has told Councils to complete urgent safety checks on similar tower blocks.
She visited the site of the fire on Latimer Road on Thursday, speaking to first responders.
"In recent months, the country has witnessed a succession of bad tragedies", she said. "However, there may be other people who were in there on the night that others were not aware were there", he said. On Friday evening, May was interviewed by Emily Maitlis on the BBC programme "Newsnight" where she sidestepped questions over whether she misread the public mood and anger over the Grenfell fire as well as what her personal response is - leading to more criticism of being called "robotic" and "cold".
During her visit residents were chanting "get her out" as police held back the angry crowd.
She 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.?"
"People have lost their lives, people have had their homes destroyed, they have fled for their lives with absolutely nothing".
Dozens of protesters also stormed Kensington and Chelsea town hall on Friday shouting "we want justice" and "not 17" - referring to the previously announced official number of dead, which has now risen to 30.
"[This aims] to give the victims the immediate support they need to care for themselves and for loved ones", Ms May said.More news: Dems defeat GOP in baseball game, give trophy to Scalise
They added that local residents should be "consulted at all stages and that we should be listened to" in dealing with the fallout from the tragedy.
The protesters barged their way through an automatic door at Kensington and Chelsea council town hall and sought to gain entry to an upper floor.
Everybody is. It's not to say it is unfair on us but I mean, we were put in a situation.
Police barred their way and scuffles broke out. A larger crowd of people remained outside.
He said it will take "weeks or longer" to recover and identify all the dead in the social housing building that was left charred and gutted by the devastating blaze.
Ms May, who was criticised a day earlier for not meeting with locals and survivors, visited the area again on Friday to meet with some locals inside a church.
Residents and neighbours are demanding answers for how the blaze spread so quickly amid reports that contractors installed a cheaper, less flame-resistant type of exterior panelling in a renovation of Grenfell Tower that ended in May 2016.