Almost two million families are being sent letters warning that "cash-starved" schools must be given more funding.
The letters, urging parents to continue campaigning for a growing funding gap to be plugged, are being sent by headteachers at around 4,000 state schools in England, covering 17 councils.
The call comes on the day the Government sets outs its legislative agenda in the Queen's Speech.
School funding was a key election issue, with school leaders, parents and unions all warning the nation's state schools are facing a severe squeeze on budgets, with many schools saying they will have to take action such as cutting staff and subjects.
The letter will be sent to parents in Northamptonshire, Cambridgeshire, Essex, Thurrock, Hertfordshire, Peterborough, Norfolk and Suffolk, the BBC reported.
It acknowledges the Conservative election manifesto pledge to find an extra £4 billion for school funding over the next five years.
But the letter goes on to say that school funding, and teacher shortages, are having "a profoundly negative effect on school provision".
It says: "It is crucial that the new Government responds quickly and effectively to a growing crisis in our schools."
The letter highlights a recent paper by the Institute for Fiscal Studies which concluded that once rising student numbers and inflation are taken into account, the additional £4 billion would still lead to a real terms cut in per pupil funding between 2016 and 2022.
"The only way for our cash-starved schools to function effectively is for proper investment - capital/buildings and revenue - to be made into existing schools. The Government must also avoid giving schools additional money through a new formula and then taking it back again through 'hidden costs' and stealth taxes."
It says headteachers will "make the strongest representations to local MPs to ensure all our schools receive adequate funding" and continue to encourage parents to "campaign vigorously to secure adequate school funding".
The Tory manifesto pledged the extra school funding would be found, at least in part, through scrapping universal free meals for infants and introducing the cheaper option of free school breakfasts for primary school pupils. It is not yet known if this policy will be taken forward.
A Department for Education spokeswoman said: "The core schools budget has been protected in real terms since 2010 and is set to rise from £41 billion in 2017-18 to over £42 billion in 2019-20 with increasing pupil numbers. But we recognise that schools are facing cost pressures and will continue to provide support to help them use their funding in cost effective ways."