Education Secretary Michael Gove is to set out plans that he hopes will end illiteracy within a generation.
Mr Gove will put forward a framework to "save lives which are currently wasted" by a lack of basic skills, The Times said.
His pledge will reportedly be put forward for inclusion in the next Conservative manifesto and is likely to be included in a first draft of ideas that will be submitted to David Cameron by Jo Johnson, the chairman of the Prime Minister's policy board.
The commitment would see plans to ensure that all children leave school with strong reading and maths skills.
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The privately-owned high-rise block is one of 228 across the country which failed fire safety tests.
Theresa May is to make the announcement during talks in Berkshire with President Emmanuel Macron on Thursday.