Croydon heads say they face budget deficits of up to pound;750,000 that are likely to force redundancies, and this means that a shorter week is necessary to reduce the burden on existing staff.
Schools in the south London borough are also considering increased class sizes, slashing subjects from the curriculum and stopping staff training.
They are pursuing a judicial review of the budget-setting process.
David Hart, National Association of Head Teachers' general secretary, said Croydon was only the "tip of the iceberg". Members from across the country had already contacted him requesting support for action, ranging from the deliberate setting of deficit budgets to refusals to implement the workload agreement.
He warned of a "serious clash" in the summer and said he would put pressure on the Government to deliver its side of the workload bargain. "A lot of headteachers will say, 'Why should we be forced to struggle to implement a workload agreement when the Government is blatantly failing to meet its own obligations under the deal?'."
The Secondary Heads Association also reported complaints from heads about lack of money for the workload agreement.
A Croydon council spokeswoman said the borough's heads were being "alarmist" but that there was a significant budget shortfall.
A spokesman for the Department for Education and Skills said Croydon had received a 4.9 per cent increase in its education funding and there was no need for schools to resort to four-day weeks.