The prospect of a nationwide teachers’ strike is looming larger after a leader of the country’s largest teaching union, backed by the Labour leadership, called on members to vote for a walkout in protest at the government’s funding plans.

Flanked by Jeremy Corbyn and the shadow education secretary, Angela Rayner, the joint head of the National Education Union (NEU) told campaigners the government would listen to nothing short of a strike and implored them to vote for one in the union’s indicative ballot.

“From today, the campaign continues. We are ramping it up,” Kevin Courtney told a rally in Westminster on Tuesday evening. “We are grateful for the support of politicians from all political parties who will support us. We know we have support from Labour’s frontbench directly here and we thank them again for that. But we say it’s our actions that make the difference.”

We know the price of beer and a pint of milk. Why not the cost of educating a child? | Laura McInerney Read more

The NEU had said it would consult its members on what action to take after saying the government’s budget promises at the end of last month did not go far enough. But Courtney’s language marked an escalation in the row.

His speech came only hours after it was announced that hundreds of college lecturers would stage a two-day strike in a dispute over pay, with more set to be balloted for industrial action.

Courtney insisted that the NEU was not “strike-happy”, saying: “We have taken every other step that we can think of … We really, really don’t want to take strike action. But they aren’t listening to any other things that we have done.”

He echoed the claim he made at the trade union’s conference in April that many parents would support a teacher walkout because they had become increasingly aware of the effects of government funding decisions on schools.

That criticism was renewed last month when, during his budget speech, the chancellor, Philip Hammond, said schools in England could use the £400m he had awarded them – a figure dismissed as insufficient by teaching unions – to “buy the little extras they need”. He exacerbated the situation later by describing the money as a “nice gesture” that could buy a “whiteboard, a couple of computers, whatever it is [headteachers] want to buy”.

Addressing Tuesday’s rally, Corbyn mocked Hammond, asking the attendees if they were “spending the money wisely” and joking: “Has it bought you a new gate, a new computer?”

Earlier, Rayner said a Labour government would not “spend, spend, spend – we will invest, invest, invest” in education. And Corbyn underlined that his party still intended to increase corporation tax to pay for the scrapping of university tuition fees, should it form a government.

Courtney attacked education ministers for having claimed that resources had been increased. While the NEU’s joint general secretary admitted that there were more teachers and that budgets were greater in nominal terms, he insisted that the increasing burden placed on schools meant these represented real terms cuts.

A Department for Education spokesman said: “Children only have one chance at an education; they all deserve the best. Since 2010, we’ve raised standards in thousands of classrooms, protected school funding and made it fairer across the country, and recently boosted budgets by £508m to give hardworking teachers a pay increase.

“While there is more money going into our schools than ever before, we recognise the budgeting challenges schools face and that we are asking them to do more. That’s why we’re supporting schools and headteachers to make the most of every pound.”