“I hold my hands up for that. I take responsibility,” she said. “And I am sorry.”
But she warned her ministers, who sat in front of her, that it was time to “shape up and give the country the government it needs”.
“Working people up and down this land… must be our only focus,” she said.
As she spoke, Johnson was embroiled in another row, this time over Libya, following comments he made at a fringe event on Tuesday evening.
He said the conflict-torn country could become a magnet for tourists and investors if it can “clear the dead bodies away” first.
– No deal on Brexit? –
After her tired appearance this week forced her to deny she was “miserable”, May said she was driven by a desire to “root out injustice and give everyone in our country a voice”.
She promised to fight to ensure “that each new generation should be able to build a better future”.
May announced a £2 billion (2.25 billion euros/$2.65 billion) investment in housing, promising to dedicate her premiership to tackling the shortage of affordable homes.
She also promised to fulfil a manifesto pledge to put a price cap on energy bills.
May had little to say on Brexit, even as the negotiations with Brussels reach a crucial point in the next few weeks.
She set out her main principles in a major speech in Florence last month, but the issue continues to divide her party.
But she left open the prospect of walking away without a deal — a threat backed by rightwing Tories who have been drawing large crowds to fringe meetings this week.
“I believe it is profoundly in all our interests for the negotiations to succeed but… it is our responsibility as a government to prepare for every eventuality,” she said.