Critics have questioned why May failed to meet victims and relatives on her first visit to the Grenfell Tower - in contrast to Jeremy Corbyn, the Labour leader. Some Tories fear May's image may have been damaged irrevocably.
May admitted that the official response to the fire catastrophe "was not good enough" as the death toll exceeded that of Britain's worst fires since World War II.
In a significant admission of failure in getting to grips with the scale of the disaster, in which at least 58 people are now feared dead, 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".
She added: "I have heard the concerns and I have ordered immediate action across the board to help victims' relatives and the survivors."
The Prime Minister met victims of the disaster at No 10 for two and a half hours. May announced that the cost for victims of legal representation at the public inquiry would be met by the Government. And she ordered more staff to go into the area around Grenfell Tower to assist the coordination of the relief effort.
May said: "There have been huge frustrations that people do not know who to talk to, that they can't get through on the council hotlines. I have ordered that more staff be deployed across the area."
She added: "Victims have concerns their voice will not be heard, that their many questions about this tragedy will not be answered. That is why I ordered a public inquiry, [which] will be open and transparent."
But families who met May indicated they were still angry at the slow response to their plight and her decision not to meet victims until nearly three days after the fire. Leaving the Downing Street meeting, one member of the group said: "We have had two and a half hours with the Prime Minister in the last 48 hours and spoke about demands and what we expect. You will hear from us in due course."
NIGHT OF FIRE
Last Wednesday (local time)
12.50am - Maryam Adam is woken by a neighbour saying his fourth-floor flat is on fire.
12.54am - The first emergency call made to London Fire Brigade.
1am - First fire crew arrives to "rapidly developing and incredibly complex" fire at the 24-storey building.
1.16am - Police begin evacuating residents.
1.29am - London Ambulance Service send 20 ambulance crews.
1.41am - Fabio Bebber tweets a picture of the fire, which has spread to the top floor, with the caption: "Fire consuming Grenfell Tower. People screaming for their lives. Horrible."
2.49am - 200 firefighters called to the blaze.
6.15am - 30 patients taken to five hospitals.
7.50am - London Fire Commissioner Dany Cotton says there's a "number of fatalities".
8.15am - Ambulance service says more than 50 patients taken to hospital, 100 medics working at fire.
11.16am - Police say six people have died, expect the figure to rise.
11.45am - Ambulance service says 64 patients taken to hospital, 20 critical.
11.59am - Rydon, which refurbished Grenfell Tower last year says it's "shocked to hear of the devastating fire".
5.00pm - Death toll increases to 12, police say recovery operation will be "long and complex".
8.22pm - Prime Minister Theresa May says there will be a "proper investigation".
- Additional reporting: PA, AAP
