Thousands of schools are likely to close after headteachers overwhelmingly backed a national walkout over the government's public sector pension plans.

Members of the National Association of Head Teachers (NAHT) voted in favour of strike action. The union balloted 24,000 members who are in the teachers' pension scheme.

While the absence of a headteacher for a day would not necessarily lead to a school closure, the vote is likely to affect millions of children as the heads are expected to co-ordinate strike action with teaching unions on the TUC's day of action at the end of this month.

The union says the government's plans will leave teachers working longer, paying more and receiving less when they retire.

Turnout for the ballot was 53.6%, with 75.8% in favour of strike action, the NAHT said.

The NAHT's general secretary, Russell Hobby, and the union's national executive would now consider the union's next move, and heads have not yet been called out on strike.

It is the first time in the union's 114-year history that members have voted to strike.

NAHT members hold leadership positions in most special schools, 85% of primary schools and more than 40% of secondary schools. They include heads, deputies and assistant heads.

Hobby said that in many ways, the result was an "unhappy milestone".

"I have spoken at length to many school leaders and not one has been anything other than upset and sometimes downright angry that they have been forced into this situation as the only way to stand up for the profession and standards.

"We welcome the government's recent concessions as marking, finally, the start of genuine negotiations. It is sad that it has taken this long, but it is a start.

"We would like to avoid action if at all possible and will be negotiating intensely and in good faith in the runup to the 30th."

He added: "Teachers are already doing their bit to address the economic downturn by accepting a pay freeze and sharing the burdens of a strapped economy along with every other taxpayer.

"The pay freeze is saving the government hundreds of millions. The proposed cuts are unfair, ill-thought-through and purely being used to pay for the mistakes of the financial sector."

Ministers argue that changes to public sector pensions are necessary to ensure the schemes are sustainable for the future.

The schools minister Nick Gibb said reforms to public sector pensions were essential as life expectancy rose.

He said: "The cost to the taxpayer of teacher pensions is already forecast to double from £5bn in 2006 to £10bn in 2016 and will carrying on rising rapidly as life expectancy continues to improve."

Gibb said the government had put forward an improved offer that guaranteed existing pension rights; gave teachers a defined, index-linked pension; and protected those closest to retirement from changes.

"We are continuing to hold serious discussions about the reforms with the teaching profession," he said.

"It is right that the unions look very carefully at what is on the table before taking industrial action."