Theresa May insisted she will defy opposition to push through her plans for a new generation of selective grammar schools in the state system.
The proposals have come under fire from experts, opposition MPs and some of her Tory colleagues - including former education secretary Nicky Morgan - but the Prime Minister insisted she would build a school system that works for all.
But Mrs May recognised that she would face a battle to get her plans through a potentially hostile Parliament, saying "no doubt there will be opposition to overcome".
The Prime Minister unveiled proposals on Friday to lift the long-standing ban on new grammars - with a £50 million annual Government subsidy to support new places - in a speech outlining her ambition to make Britain "the great meritocracy of the world".
But her ideas for England's schools were attacked by educationalists including the Ofsted chief inspector Sir Michael Wilshaw, who accused her of trying to "put the clock back" in a way which would halt momentum towards better results in the state system.
And Ms Morgan - who was sacked from the education brief in July - warned that increased selection by ability would be "at best a distraction from crucial reforms to raise standards and narrow the attainment gap and at worst risk actively undermining six years of progressive education reform".
Mrs May should instead build on the academy and free school reforms pursued under David Cameron, which were creating "a truly comprehensive school system in which every child is able to achieve excellence", the former education secretary said.
Ms Morgan's comments follow expressions of concern from other influential members of Mrs May's own Conservative Party, including Commons Education Committee chair Neil Carmichael and Health Committee chair Sarah Wollaston, in an indication of the difficulty the PM may face forcing her radical reforms through Parliament.
Backbench Tory MP Karen Lumley said: "I am very sceptical about the idea that poor children will benefit from a return to grammar schools. This could lead to a divisive system and put the clock back on education, negating much of the great progress we have made over the last few years."
Labour have pledged to fight the grammar school plans "every step of the way", while Liberal Democrat leader Tim Farron predicted the "out-of-date, ineffective approach" would be defeated in the House of Lords, where Mrs May does not enjoy a majority.
The plans are particularly vulnerable in the upper chamber because they were not included in the 2015 Tory manifesto, denying Mrs May powers to overrule peers.
Writing in the Daily Mail, Mrs May insisted her plans would give parents the chance to send their children to a "great school".
"I was incredibly lucky when I was a young girl growing up," she said. "My education was varied: I went to a grammar school that became a comprehensive - and for a short time I attended a private school.
"I know too that my teachers made me the woman I am today. I want every child to have the kind of opportunities that I enjoyed.
"I want every parent to have the peace of mind that comes with knowing their children will get the chance to go to a great school.
"And I want every teacher and every school to have the resources and the capacity to deliver on those promises.
"I know these things will not happen overnight. They require bold decisions and a lot of hard work, and no doubt there will be opposition to overcome.
"But I am determined that we will build a school system that works for everyone. That is a hallmark of a truly meritocratic Britain."
The reforms outlined by Mrs May include:
:: Requirements for grammars to promote social mobility, by taking a proportion of pupils from lower-income backgrounds or opening "feeder" primaries in disadvantaged areas;
:: Lifting the cap on faith schools taking pupils from their own religious community;
:: Tougher public benefit tests for independent schools to retain their charitable status;
:: Demands on universities to sponsor state schools or set up free schools.
New-style "smart" exams would identify pupils with "true potential", rather than allowing middle-class parents to ensure their children a grammar school place through expensive tutoring, she said.
And she announced plans for grammar school entry at 14 and 16 as well as 11, to avoid the danger of late-developing children being written off as non-academic at the start of their secondary careers.