The union said pay cuts and high workload are hitting teacher recruitment and retention hard, and causing damage to education.
It said the Government’s previous proposed three per cent pay increase for teachers would mean a “huge pay cut” in reality.
The NEU said if Mr Zahawi does not meet their demands it will launch an indicative ballot in the autumn term, possibly leading to a formal ballot on strike action.
The letter, signed by NEU joint general secretaries Mary Bousted and Kevin Courtney, said: “We calculate that teacher pay has fallen by a fifth in real terms since 2010, even before the effects of this latest bout of inflation … Alongside the decline in teacher pay in real terms against inflation, it has also declined in relative terms against earnings. Average teacher salaries are at their lowest level compared to average earnings across the economy in over 40 years.”
They added: “We have to tell you that failing sufficient action by you, in the autumn term we will consult our members on their willingness to take industrial action.
“And we will be strongly encouraging them to vote yes. We can no longer stand by while you run both education and educators into the ground.”
It comes as the country is braced for a summer of strikes by postal workers, barristers, rail workers and NHS staff.
Barristers are set to walkout on Monday in an ongoing row over legal aid funding.
Rail workers are set to strike again tomorrow and on Saturday in their dispute over jobs, pay and conditions.
Meanwhile NHS staff up to nursing level are set to receive their annual pay offer this month. Unison has threatened strike action if pay does not at least match inflation.
* Holland Park School was closed for the ninth day on Wednesday as teachers walked out in a dispute about plans to turn it into an academy. A further three days of strikes are scheduled for next week.