Hundreds of thousands of people joined rallies, picket lines and marches across England and Wales on Thursday as wealthy ministers were warned not to demonise the UK's lowest paid workers.

School workers and firefighters took to the streets alongside care workers, refuse collectors and other local government employees to protest against real terms pay cuts and falling living standards.

The strike was part of the biggest round of industrial action in the UK for three years and prompted a bitter political row over Tory plans to tighten strike laws.

Vince Cable, the business secretary, attacked David Cameron's plans to raise the threshold for strikes, which could only be legal if supported by a majority of a union's membership, not just those who vote.

Cable said ministers were attempting to "undermine basic workers' rights". "Trade unions should not need approval for a strike from half their members when MPs do not need to reach such a high threshold to get elected."

"We disagree with the Tories' assertion that a small turnout in strike-action ballots undermines the basic legitimacy of the strike," he said. "If they want to look at minimum turnout this would have major implications for other democratic turnouts and elections. Many MPs have been elected by well under 50% of their electorate, let alone police commissioners or MEPs. Why have a threshold in a ballot but not make our elected politicians or shareholders face the same hurdle?"

David Cameron's official spokesman said on Thursday night that public sector strike action is always wrong.

The Labour party had refused to back the strike, but shadow Cabinet Office minister Michael Dugher said the government had to take much of the blame for the dispute and labelled ministers' belligerent stance towards low paid workers as "pathetic". He said: "We have had yet another depressing demonstration of a cabinet full of millionaires demonising the lowest paid in society."

Addressing Francis Maude, the Cabinet Office minister, Dugher added: "You remind me of a man trying to fight everyone in the pub at the same time. But when the country needs to see a negotiated settlement, what have we got? Ministerial belligerence revelling in confrontation, where strike action by the unions is almost a public policy success for a government desperate for a fight. It's sabre-rattling, it's union bashing, it's playing politics, it's a deliberate distraction and frankly it's pathetic."

Union leaders criticised the Labour party for not backing the strike. Dave Prentis, the leader of Unison, said: "It is time for Labour to make up its mind. Public service workers are people who should be Labour's natural supporters and they deserve Labour's unashamed backing in return."

Hundreds of rallies, marches and pickets took place at schools, council offices and town and city centres across the country. In London thousands of workers descended on Trafalgar Square. Firefighters, wearing T-shirts with the slogan "We save lives – not banks", listened as union leaders told the crowd that the government was trying to run down public-sector wages and the services that staff provide.

Charles Brown, a 52-year-old firefighter from London, said: "They want us to work longer, pay more in [to our pensions] and get less out … we have tried to have negotiations with the government but they are not listening, so we have no option but to strike."

Nagour Zahri, a teacher from east London, said: "We are not feeling the economic recovery like everyone else. In fact it feels worse. The fact is we are losing teachers, good teachers."

Hundreds of schools were closed and museums, libraries, art galleries and tips shut for the day. In Bristol burials and cremations were suspended and few boats were allowed into the city's historic floating harbour.

Primary school teacher Sheila Caffrey said about half the staff at her school in south Bristol, were out. "I'm on strike because the government keeps moving the goalposts. It's all about ticking boxes rather than educating children. It's more about me proving I'm a better teacher than the next one rather than really trying to do the best for the children."

Maude said curbing public-sector pay was necessary to pay the UK's debts and insisted the lowest paid workers had been protected. He said support for public sector strikes had fallen over the past four years. "This is the fourth one-day public sector strike in the last few years," he told the Commons. "The proportion of public sector workers going on strike has fallen on each occasion." In an interview for The House magazine Maude even suggested allowing parents and governors to break the teachers' strike by changing the rules to let them come in as volunteers.

However union leaders said support for Thursday's strike had been "solid." Prentis, said: "The strength of feeling amongst our local government and school support workers over the issue of pay was plain to see today. The decision to take strike action and sacrifice a day's pay was a very difficult one, particularly for the hundreds of thousands of low paid workers, but our members felt this was the only way to have their voices heard."

TUC general secretary Frances O'Grady said the strike had been "well supported" and had revealed "just how angry public servants are at plans to lock them out of sharing in the recovery until at least 2018."

She criticised Tory plans raise the threshold for strikes saying that "rather than get round the table, ministers are threatening a change in the law that would make legal strikes close to impossible."

"Instead of imposing a ballot threshold that not a single MP met in the last election, politicians should stop ignoring sensible proposals to increase secret ballot turnouts at the workplace and online."

And she warned that the public, who see the essential work low paid public sector workers do every day, would not take kindly to them being lectured by wealthy ministers who had never had to worry about paying the bills.

"It is hard to see how an offer to depress living standards for these people for the foreseeable future and then to try and stop people doing anything about it will win votes at the next election."