The National Union of Teachers has voted to hold a national strike in June, with the possibility of more walkouts to come, as it also backed plans to investigate a boycott of new primary school tests.

To chants of "Gove must go!", NUT delegates at their annual conference in Brighton overwhelmingly voted on Monday for a motion calling for a national campaign on pay and working conditions, including lobbying MPs in marginal seats, a national rally and a strike to take place in the week beginning 23 June if "significant" progress was not made in negotiations with the government.

After an acrimonious debate over more aggressive action – including a pair of two-day strikes later in the year – the conference backed an amendment that stiffened the language to include consultations on "a series of strikes through the autumn term and into 2015".

The successful amendment also said the union should seek to co-ordinate with other public sector unions – such as NHS workers – in taking industrial action.

Teachers also denounced plans to introduce a new national assessment for four- and five-year-olds at the start of formal schooling, claiming that it would damage pupils, force schools into competition and distort teaching at a crucial stage.

The conference backed motions that called for efforts to oppose the baseline assessment that the Department for Education is proposing for children in England at the start of reception year.

The motion on early years and primary assessment said the tests were "devised to entrench a system of league tables that sets schools in competition with each other", while an added amendment called for "the possibility of a mass campaign of principled non-compliance" in response.

Speakers argued that children in early years education – from the ages of three until seven - learned better through the use of informal play and would be harmed by the early imposition of formal teaching.

Stephane Bernard, a teacher from Lambeth, told the conference that she was "shocked, outraged, horrified and angry" to hear about the plans for more testing.

"What our four- and five-year-olds need is not another barrage of tests but emphasis on the child's personal, social and emotional development, communication and language skills. They need nurturing and their physical skills developing. All these things are key," Bernard said.

"Since coming to office, the coalition government has continually trivialised the importance of health and safety, claiming that it has imposed unnecessary bureaucratic burdens on schools," said Chris Keates, general secretary of the NASUWT.

After the motion endorsing strikes was passed, the NUT's general secretary, Christine Blower, said: "The union will demand that Michael Gove attends talks with the unions to discuss his education policies, on workload and accountability, teacher pay – including performance-related pay– and his unfair pension changes.

"If the strike happens it will be Michael Gove's fault," she said.

The prospects of further joint action with the NASUWT – the other main teaching union – appear to have receded though, after the NASUWT took a softer line in its own motion on industrial action at its annual conference in Birmingham. It stopped short of specifically calling for a timetable for strikes.

Although the two unions have taken combined action in the past, the NASUWT declined to take part in the NUT's most recent national strike on 26 March.

Anne Lemon, an NUT executive member who backed the motion, told delegates in Brighton: "Yes, we want to involve as many teachers as possible. But if we can't take our NASUWT colleagues with us then we have the commitment and the ability to go it alone.

"Very importantly, the motion does not exclude us from taking strike action with other unions that will be coming out. If that means taking more than one day then there's nothing that precludes that in this motion."

Lemon suggested that if joint action was taken, "400,000 nurses along with 300,000 teachers will send a very clear message to this government".

The NASUWT members voted for a motion on Sunday backing the union's leadership to take "action short of strike action" as well as "strike action at school, local, regional and national level as appropriate", without fixing specific dates.

On the prospects for joint action, the motion merely said the NASUWT's strategy would be to "continue to campaign with other unions in the TUC", without naming its sister union.

Chris Keates, the NASUWT general secretary, did hold out a sliver of hope for co-ordinated action, saying: "We have no plans for naming days in any month. That doesn't mean to say there won't be an escalation of action in either the summer term or the autumn term if sufficient progress wasn't made in talks with the DfE."

A Department for Education spokesperson said: "Further strike action will only disrupt parents' lives, hold back children's education and damage the reputation of the profession."

Earlier on Monday, the NUT conference declined to change its timetable and hear a priority motion on the "Trojan Horse" investigation into schools in Birmingham. Speakers against the move to debate a motion argued that too little was known about what was going on in Birmingham, and much of it was innuendo and rumour.

The proposed motion said in part: "Conference resolves to condemn the Islamophobia that has been whipped up by the press and media regarding Operation Trojan Horse and Birmingham schools."