There is "widespread anxiety" among headteachers that schools will be unfairly judged by the use of new pupil wellbeing indicators.
Schools fear they will be criticised for aspects of pupil wellbeing over which they have little or no control, according the Association of School and College Leaders (ASCL).
Ofsted and the Government want to introduce a new range of indicators to make up for a perceived lack of data.
Teachers' leaders reacted angrily last year when early discussions raised the possibility of schools being held to account over teenage pregnancy and obesity rates.
An Ofsted consultation on the proposed indicators, which closes today, has stressed that the inspectorate has "no intentions" of using those measures.
But under the proposals, new information will be published about school performance, including attendance figures, rates of persistent absenteeism and take-up of school lunches.
Parents and pupils will be surveyed to find out their views on school performance, including how well they promote healthy eating and how successful they are at making pupils feel safe.
School will be encouraged to make all the results public and they will be published by Ofsted following school inspections. The results will be used to create local authority-wide data about wellbeing.
Launching the consultation last year, children's minister Baroness Delyth Morgan said: "These indicators are not an extra burden but additional tools to help schools improve their wider role in their communities.
"They will build on data about pupils' attainment and progress, so wider aspects of children's lives can be benchmarked."
But ASCL has heavily criticised the plans and said that no new numerical targets for schools should be introduced.
John Dunford, general secretary, said: "My fear is that numerical indicators will get used because they are easy and available.
"The information schools already gets from surveying parents and pupils is very helpful in driving school improvement. When that moves into the realms of external accountability it is new territory."
All of the factors proposed were highly correlated with social deprivation, the union said.
It raised concerns that the suggested system for carrying out the surveys was "frighteningly bureaucratic" and took too much control away from schools. "Unless this is handled with extreme sensitivity, this could mark the beginning of the end of self-evaluation as schools will come to regard it as something being done to them," the union said to Ofsted.
It also suggested that Government plans to introduce a "balanced scorecard", which would give schools a grade for their overall performance, made plans for figures on pupils wellbeing redundant.
But Ed Balls, the schools secretary, said the two systems could work hand in hand.
"Wellbeing indicators will be at the centre of the report card," Mr Balls told the TES.
"It will be one of the most important things, alongside achievement in key qualifications.
"The report card will not replace the wellbeing indicators. It will be a place where they are clear to see."