Nearly 200,000 National Education Union (NEU) members voted by 98% to 2% to reject the government's offer of a £1,000 one-off payment and a 4.5% pay rise next year.
It was the highest rate of opposition in the union's recent history, higher even than the 90% vote in favour of strike action in the NEU's formal ballot in January.
After the result was announced, delegates at the NEU's annual conference in Harrogate taunted the education secretary, Gillian Keegan, chanting: "Come on Gill, pay the bill."
Kevin Courtney, the NEU's joint general secretary, said: "The strength of this vote is completely unprecedented for a teaching union in the UK in modern times. There was anger in September, when the NEU's campaign began, but I think this vote shows a step change to fury. It reflects a determination among teachers that things cannot go on as they are.
"This result cannot be batted away with glib dismissals from the Department for Education. This is a very clear, unambiguous message from almost 200,000 voters. This is the profession telling the education secretary that her offer is insulting and will not do."
The result puts the NEU on a collision course with the government, with Keegan and Downing Street saying the vote means the £1,000 payment will be withdrawn and next year's pay deal will be set by the independent School Teachers' Review Body, which makes recommendations to the government.
The result will also trigger two more days of strike action, likely to close schools around England, on Thursday 27 April and Tuesday 2 May. The annual conference will debate a motion calling for a ballot on further strikes in the autumn, which seems almost certain to pass given the strength of feeling among delegates.
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