Ministers are being asked to order urgent checks of fire safety measures in England's schools.
The National Union of Teachers, Fire Brigades Union and Association of Teachers and Lecturers are calling for cladding to be analysed urgently, in the wake of the Grenfell fire.
The unions also asked for clarity on whether plans to water down fire safety rules for schools were being scrapped.
Ministers say cladding on schools over four storeys high is being checked.
And the government insisted there were no plans to bring in any changes which would make fire safety laws less strict.
The unions made their call for fire safety action in a letter to Education Secretary Justine Greening.
They asked her to publish a list of all schools that had been fitted with cladding that needed to be removed, as well as a timetable for removal.
They also asked for ministers to bring forward legislation to require sprinklers to be fitted to all new schools.
Fire safety guidance for schools, known as Building Bulletin 100, had required all new schools to be fitted with sprinklers – except for a few low-risk schools, the letter highlights.
Despite this, only 35% of new schools built since 2010 – when the coalition government came to power – had been fitted with sprinklers.
This compared with 70% of schools built between 2007 and 2010.
In a statement, the unions said: "It is clear that current guidance is being ignored in the rush to build new schools as cheaply as possible."
Kevin Courtney, National Union of Teachers general secretary, said: "For far too long the government has viewed health and safety as a 'red tape' burden.
"It has been seen as an afterthought and an opportunity to try to cut corners and save money.
"We all now know the terrible consequences of that approach. Fire safety in schools must now become a priority and for this to happen the government needs to heed our advice."
The national school-building programme, Building Schools for the Future, was scrapped by the then Education Secretary Michael Gove in 2010 for being "wasteful" and too expensive.
A new programme for school building was developed which the then government said was more efficient and less costly.
And scores of free schools have since been opened up in buildings not previously used as schools.
The Local Government Association said that fire safety checks were continuing in council-run schools, with Friday the deadline for completion.
Nick Gibb said: "The government is taking the potential impact from the Grenfell Tower seriously and as such, we are taking a strategic approach to the assessment of the wider public sector estate.
"The department is undertaking an analysis of all school buildings to identify those over four storeys high, to ensure we include all buildings that are over 18m in our analysis.
"This analysis is to establish what, if any, external cladding has been used on these buildings."
A Department for Education spokesman said all schools had to have mandatory fire risk assessments and new schools were subject to additional checks during the design process.
Where these additional checks say that sprinklers or other fire safety issues are required, such steps must be taken.