In her final TV interview with political editor Laura Kuenssberg, the PM spoke of “frustration” at not seeing Brexit through and underestimating how “entrenched” MPs had become.
She said she had achieved an “enormous amount” in three years in the job.
But she was sorry having to leave when “there was more that I wanted to do”.
Mrs May and her husband Philip will depart Downing Street on 24 July, succeeded as prime minister by either Boris Johnson or Jeremy Hunt.
She was forced to announce her exit in May, amid a revolt by Conservative MPs angry about her failure to take the UK out of the EU on 29 March and her decision to open Brexit talks with Labour.
Interviewed in 10 Downing Street, Mrs May said she “didn’t recognise” herself in criticisms that have been made of her personality and leadership.
But, despite having to go earlier than she wanted, she insisted she had been the “right person” for the job and was “immensely proud” of what she had accomplished.
Asked if she could have done more to persuade MPs to back her Brexit deal with the EU – which they rejected three times – she replied: “One could always look back and say, ‘If I’d sat down and talked to people more often’.”
Mrs May said she had wrongly assumed MPs would be “eager to get Brexit over the line”.
“I actually think there’s quite a difference between Parliament and the public,” she said. “I think the public have got a very simple view. A decision was taken – just get on with it – and they are not in that same polarised way that Parliament has been about this issue.”
It had been, she said, “incredibly frustrating” that MPs on either side of the Leave-Remain divide had “got so sort of entrenched that they just were not willing to make that compromise that would enable us to get the majority to get this through”.
Mrs May would not be drawn on whether she was planning to back Mr Hunt or Mr Johnson as her replacement, saying only that “they understand the responsibility that this job brings”.
While wishing her successor well, she said she would continue to argue that leaving the EU “with a good deal” was vital.
And she called for a more discipline in government after years of leaks and political disagreements inside her cabinet: “Good government depends on collective responsibility. It needs to return.”
‘Not really me’
During the interview, Mrs May opened up about life in Downing Street and the emotional strains of the job, recalling the “chilling” moment she was told about the Manchester Arena bombing in 2017.
She said she did not regret calling a snap general election during the same year, in which she ended up losing her Commons majority.
But Mrs May conceded she had made mistakes during the campaign, including not appearing in a TV debate with other party leaders, with the then Home Secretary, Amber Rudd, taking part instead.
“I regret running a campaign that wasn’t really me,” she said. “There are other things – I think I probably actually should have done the TV debates.”
Mrs May, who will remain in Parliament as MP for Maidenhead after leaving Downing Street, defended her economic record, saying unemployment was at a record low and austerity was coming to an end.
She also hailed the progress made in tackling some of the “burning injustices” she highlighted in her first speech after becoming prime minister.
Mrs May said she was proud of “championing some causes that otherwise will be unfashionable”, such as the fight against modern slavery and domestic violence and mental health support.
“Brexit has taken up a lot of people’s thinking, but actually there’s an enormous amount that has been done behind that.”
She said she hoped her critics and supporters alike would feel that “in everything I’ve done, I’ve always done what I believed to be in the national interest”.
The winner of the Conservative Party leadership race – and next prime minister – will be announced on 23 July.
Either Mr Hunt or Mr Johnson will take over from Mrs May the next day.
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