The ballot had been called for against the wishes of Doug McAvoy, general secretary, at the union's annual conference at Easter. Mr McAvoy suffered a series of defeats at the hands of the Left, and later accused extremists of taking over the union. Mr McAvoy was also embarrassed by activists who were involved in a scuffle when David Blunkett, Labour's education spokesman, arrived at Blackpool to speak at an invitation-only meeting.
The anti-strike vote - more than four to one on a turn-out of 51 per cent - was claimed as a victory for democracy by Mr McAvoy. He said the result proved that ordinary members were not in step with those from the hard Left who dominated conference. "It clearly indicates that many of the delegates voting in Blackpool were doing so in furtherance of their political agenda," he said.
He said that the wider membership may also be surveyed over a number of issues before next year's conference, to guard against unrepresentative votes by delegates.
The union will support local action in schools which members say have classes that are too large.
The result was welcomed by David Blunkett and the Department for Education. Margaret Morrissey, spokeswoman for the National Confederation of Parent-Teacher Associations, which had been prepared to support a one-day strike, said: "Parents will be even more determined to go forward with teachers in support of their campaign on class sizes."
But left-wing members of the NUT's national executive accused Mr McAvoy of unduly influencing the result, and called for his conduct during the ballot to be investigated.
The National Association of Schoolmasters Union of Women Teachers is consulting its members on what type of action to take over class size. Voting forms have been sent out asking whether members believe oversized classes lead to unreasonable workloads and whether they would be prepared, once all other avenues had failed, to take strike action.
Nigel de Gruchy, general secretary, said: "This is not a ballot for industrial action. It's an exercise to gauge members' views. We have started a massive training programme for all our school representatives. They will be given the information and expertise they will need to engage in discussions on workload and class size with school management."
More than a million primary school children are taught in classes of 30 and above.
In a message to NUT members in the run-up to the ballot, Mr McAvoy said that he believed a joint campaign with parents and governors was a more appropriate way of showing anger against class size than a one-day strike. He claimed a strike would "alienate those whose support we most need".