The leader of one of the four unions involved in a national strike has said that the government will be "proved wrong" in its predictions that few will walkout in protest at an overhaul of public sector pensions.

Mark Serwotka, general secretary of the Public and Commercial Services union said "hundreds and hundreds of thousands" were expected to take part in Thursday's strikes because the government was "failing to compromise" over pension reforms that he claimed were unfair and politically motivated.

Picket lines were mounted outside schools, government buildings, jobcentres and courts today by striking public sector workers in the biggest wave of industrial unrest since the coalition was formed.

Union leaders said early indications were that the 24-hour walkout by the National Union of Teachers (NUT), Association of Teachers and Lecturers (ATL), University and College Union and the PCS, which between them cover 750,000 public sector workers, was being strongly supported.

A third of schools are expected to close and two-thirds of universities have cancelled lectures. Benefits will go unpaid, court cases will be postponed, police leave has been cancelled in London and airports are bracing themselves for backlogs at immigration.

But the decision to go out on strike while talks with the government are ongoing were criticised both by deputy prime minister Nick Clegg and Labour's Tessa Jowell as members up and down the country joined picket lines. Boris Johnson, the Conservative mayor for London, reiterated his call for strike laws to be tightened to take action to protect the public, as well as those workers who do not vote for strikes.

Francis Maude, cabinet office minister, insisted that early indications from airports and ports showed that fewer members were heeding the "inflamed call" for mass walkouts.

"More are turning up for work and we are maintaining a much better service than we expected to be able to," Maude told the BBC Radio 4 Today programme.

Maude and Serwotka became embroiled in a war of words over the airwaves this morning, as the government claims that the public sector pension schemes were "unaffordable" came under scrutiny.

The Conservative minister insisted that Lord Hutton, the former pensions secretary who drew up recommendations for reforms, had said "very clearly" that the status quo was "not tenable".

"You cannot continue to have more and more people in retirement being supported by fewer and fewer people in work," said Maude. Long-term reform is needed."

Pressed on the fact that Hutton's report made no such claim, Maude insisted that the fact was that the costs of pensions would become unaffordable unless changes were introduced.

Yet, Serwotka said that the Hutton report included a graph which clearly shows that the cost of the pension scheme is falling in terms of GDP.

Serwotka accused the minister of "floundering" when scrutinised about the government's plans.

"The National Audit Office, the public accounts committee, the Institute for Fiscal Studies, everybody accepts that's not the case. The cost is going to fall over the next 40 years. So it's not about affordability, so then they try to move the goalposts and say it's about being untenable," he said.

Serwotka said the government's "real agenda" was trying to create a "race to the bottom" on pensions.

"This is what it is really all about," he said. "You are trying to cut public sector pensions and the reason you are floundering this morning is that you are trying to mislead people." The cabinet was full of people like Maude, in a "very privileged position", trying to cut the pensions of public sector workers, said Serwotka.

"That is why hundreds of thousands of people are on strike, because it is unfair and unjust."

Maude condemned leaders taking members out on strike while colleagues were awaiting the outcome of the talks. Serwotka was "writing himself out of the script, when there is so much to talk about," he said.

But Serwotka fired back that the government had made clear that its mind was already made up: "Whenever I've asked him, will the government compromise on any of the central issues in the dispute – work up to eight years longer, pay 3% more, get a reduced pension and move the pensions indexation from RPI to CPI, which devalues pensions by 15% – he says on none of those will he move a jot. While we are talking, we are not negotiating."

Nick Clegg said he was disappointed that unions had gone ahead with strikes while negotiations were still going on.

"I think it's a real shame that there are strike today because there are talks which are actually ongoing between the government and the trade unions, I don't think the strikes help members of the trade union, I don't think it helps the public, I don't think they help the country at large. I think what everybody wants is for us to stick with it, carry on talking and sort this out."

Tessa Jowell, shadow cabinet office minister, also criticised the strikes.

"We're absolutely with the people of this country who should not have their services disrupted," she told BBC Breakfast.

"I'm critical of the way, as Labour is critical, of the way in which the government has handled this dispute, but these strikes today should not be taking place."

But ATL general secretary Mary Bousted said unions felt they had no choice because of the government's failure to conduct meaningful talks.

"We don't want to be on strike, and we wouldn't be on strike if the government had been prepared to do what they say they're going to do now, and that's negotiate," she told the BBC.

The valuation of the teachers' pension scheme (TPS) is two years overdue.

"How can I negotiate when I don't know the health or otherwise of my scheme?" she said. "And that's the cavalier and inept way that they have approached these negotiations. My union hasn't been on national strike throughout its history in 127 years. Do you think I would be here now if there was any other way?".

Kevin Courtney, deputy general secretary of the NUT, said the early indications were that "large numbers" of schools were affected by the action, around 80%.

"We realise that's very disruptive for parents," he said, "and we do regret that. We had hoped to reach a settlement before the industrial action, but the government isn't serious about talks."

Among the buildings being picketed was parliament, with strikers saying they hoped some leftwing MPs would refuse to cross the lines.

PCS members were stationed outside the Royal Courts of Justice – where the high court and court of appeal judges sit – in central London.

Union officials said court staff had joined the strike but they were unsure what affect the action would have on the running of the courts.

Unions were also targeting the headquarters of the education and business departments.

Police leave has been cancelled in London, where union leaders and thousands of activists will take part in a march, followed by a lunchtime rally in Westminster.

The TUC said today that millions of public sector workers were having to pay for the deficit that they did nothing to cause.

Brendan Barber, TUC general secretary, who is visiting picket lines in the south-west, will tell a rally in central London later in the day that it is "hardly surprising" that public sector workers' pay has been frozen while it was "bonuses as usual" in the financial sector.

"This is gold standard for unfairness."