Labour leader Jeremy Corbyn has criticised the Government's plans to introduce new selective schools.
Under plans unveiled by the prime minister, children will sit new selection tests aimed at assessing their "true potential", Theresa May said.
"I want good education for every child. Selectivity at 11 divides communities, divides children and ends up giving a good chance to a minority and less chance to the majority."
"I don't think that's a very sensible way forward for our country," he added.
Mrs May said schools will be urged to recruit at 14 and 16 as well as 11 to avoid the danger of children being written off as non-academic at the start of their secondary careers.
Chief Rabbi Ephraim Mirvis has backed the government's plans to end the 50% cap on the proportion of pupils selected by religion at faith schools.
He said: "For many years, without the 50% rule, the Jewish community proudly built schools which did not compromise on outstanding academic standards, an immersive Jewish atmosphere and a total commitment to promoting the values of integration and tolerance.
"I wholeheartedly support the Government's proposals, which will enable us to return to that arrangement."
Sam Freedman, executive director of programmes for charity Teach First, has said grammar schools will not support those who would "benefit most from a good education".
Reacting to Theresa May's announcementthat selective schools will be expanded, he said: "Even with quotas, by their nature grammar schools will only ever support a small proportion of children and not those who would benefit most from a good education.
"We already know the best ways to use education to support social mobility and we need to focus on making sure all pupils get an outstanding education, leaving school ready for life in a global economy."
Liberal Democrat leader Tim Farron has said Theresa May's plans for new grammar schools is "regressive".
He tweeted: "This education policy is flawed and muddled. It is regressive and divisive. It's an ideological shake up when it's not needed."
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