The Conservative leader gave a moving speech after the official state opening of Parliament on Wednesday and said the initial response to victims of the inferno that claimed at least 79 lives “was not good enough”.
“One lady I had met ran from the fire wearing nothing but a T-shirt and a pair of knickers,” she said.
“She had lost absolutely everything. So let me be absolutely clear, the support on the ground for the families in the initial hours was not good enough.
“People were left without belongings, without roofs over their heads, without even basic information about what had happened, what they should do and where they could seek help.
“That was a failure of the state, local and national, to help people when they needed it most.
“As Prime Minister, I apologise for that failure and as Prime Minister I have taken responsibility for doing what we can to put things right.”
May stressed that victims would receive payments as they attempted to rebuild their lives and pledged to rehouse those who had lost their homes within three weeks.
The apology came after May was criticised for failing to meet victims in the initial days after the blaze.
It also emerged that May spent 50 minutes at a Tory fundraiser this week. She was criticised after she spent just 15 minutes at the site of the fire during her first visit.
The Prime Minister has announced a judge-led public inquiry into the disaster and today promised that victims’ families will be consulted about the inquiry’s terms of reference.
The Metropolitan Police has confirmed 79 people died in the blaze but the death toll could yet rise.