"The response of the emergency services, NHS and the community has been heroic. But, 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," May said as quoted by the Financial Times newspaper.
May noted that she was aware of the situation and ordered immediate response to support the people on the ground.
A huge fire started at the 24-floor Grenfell tower high-rise block in North Kensington on Wednesday, engulfing the entire building and trapping almost 120 families inside. The fire prompted demonstrations in London over the way local authorities dealt with the implications of the fire. According to the latest police data, at least 58 people are still missing.
Earlier in the day, thousands of people gathered in London to protest over the lack of government response to the deadly Grenfell Tower fire along with those demonstrating May's intention to form a parliamentary coalition between the Conservative Party and the Democratic Unionist Party (DUP) following the UK snap general election.
On Friday, demonstrators gathered near the Royal Bourough of Kensington and Chelsea Council and demanded release of full information about the number of the people that lived in the Grenfell Tower, as well as full transparency of the investigation and immediate allocation of financial aid to the victims.