The chancellor is to announce extra money for new free schools in England, which could include grammars, in Wednesday’s Budget.
It comes as head teachers are protesting about a funding crisis in existing schools.
Philip Hammond will confirm a one-off payment of £320m for 140 new free schools, on top of the 500 already pledged to be created by 2020.
Labour’s Angela Rayner said schools still faced £3bn in spending cuts.
The funding announcement could pave the way for a new generation of grammar schools.
Currently, all new schools are required to be free schools, but the government has been looking at lifting a ban on opening new grammars.
This would mean some of the £320m could be used for new selective schools or to expand existing grammars.
Mr Hammond will also promise £216m to rebuild and refurbish existing schools, but he is facing criticism for failing to address the growing warnings from head teachers about a funding crisis in existing schools.
There have been warnings of four-day weeks and cuts in staffing and subjects – and the National Audit Office has warned of an 8% real-terms funding gap for schools up to 2020.
Writing in the Daily Telegraph, Prime Minister Theresa May said her “personal mission” was to increase the diversity of England’s school system.
“That means decisively shifting Britain’s education system and building a great meritocracy so that children from ordinary working families are given the chances their richer contemporaries take for granted,” she said.
She said the government would enable new selective free schools to be set up “so that the most academically gifted children get the specialist support to fulfil their potential, regardless of their family income or background”.
By Sean Coughlan, BBC News education correspondent
This funding promise sets a clear political direction of travel – making a priority of more free schools and paving the way for a new generation of grammar schools.
But it offers nothing to head teachers complaining about a funding crisis in their basic budgets.
If nothing more is forthcoming from the chancellor, Tory backbenchers, teachers’ unions and parents will be alarmed.
The spending pledges also need to be seen in the context of the scale of the financial pressures.
The chancellor is promising £216m to renovate schools – while the National Audit Office says that bringing schools up to standard would cost £6.7bn.
The £320m announced to open new schools is against a projected £3bn funding shortfall for existing schools.
But the government – balancing NHS and social care pressures – will repeat its line that school funding has been protected at a time when money is tight.
Grammar school head teachers have revealed their discussions with education ministers about how new selective schools could operate – such as providing centres of excellence for the top 10% of the ability range.
This suggested that £150m would be available for short-term bids for expanding selection.
And Mrs May is promising to put out the details of the government’s plans “in the coming weeks”.
The general secretary of the Association of Teachers and Lecturers, Dr Mary Bousted, said teachers and heads in existing state schools facing real-terms cuts would be dismayed to see the chancellor prioritising free schools and grammars.
“These spending pledges are totally insufficient to tackle the schools funding crisis the government is inflicting on schools by forcing them to make over £3bn of savings by 2020,” she said.
Teaching groups and unions have warned that their budgets have not kept pace with rising costs.
But ministers insist schools funding is at its highest level on record. Mr Hammond said the core schools budget stood at more than £40bn this year.
The Budget will also see Mr Hammond pledge to ensure children from poor backgrounds are given an entitlement to have paid travel to selective schools.
Labour’s shadow education secretary Angela Rayner said she was “really quite disgusted” by the funding plans, saying it was a “drop in the ocean” compared with the scale of cuts.
Grammar plans were a “vanity project”, she said.
Liberal Democrat education spokesman John Pugh said the Tories had their “priorities wrong” on education.
It was “unbelievable” to focus money on more free schools when the “free schools programme was shown to have overspent to the tune of £9bn”, he said.
But the New Schools Network, which supports the opening of free schools, said the funding plans were an endorsement of the quality of free schools and their popularity with parents.
They want more of them in cities, including Birmingham and Manchester.
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