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Union leaders have warned the Government that industrial action will continue into next year.
At a huge rally in Trafalgar Square, unions made it clear the action would stretch to the run-up to the general election.
Matt Wrack, leader of the Fire Brigades Union, said more strikes should be held "soon."
"What we see today is an inkling of the power that rests in the hands of working people," he said.
"We have a government destroying our public services and wrecking the lives of public servants. This is our 15th strike, and we are not giving up. There is no mood to surrender, but there is a mood to continue the fight."
National Union of Teachers general secretary Christine Blower said: "I've been getting messages from people saying that they are more determined now than they were in the past to take action."
The Department for Education said there is "no justification" for further strikes.
Unions have hit out at Conservative plans to change strike balloting laws as "utter hypocrisy".
The Conservatives are drawing up plans to change employment law so that a threshold of those balloted would have to be reached before industrial action could be held.
But Unite said no Tory Cabinet member achieved a 50 percent voting threshold in the last general election.
General secretary Len McCluskey said: "It is utter hypocrisy for the Government to talk about mandates for trade unions when not a single member of the present Cabinet would have been elected using the same criteria.
"The fact is not a single councillor in England has won 50 percent of the electorate, not a single MEP has reached the 50 percent threshold, Boris Johnson scraped in with just 37 percent in 2008 and the Government's flagship police and crime commissioner election gained a risible 17 percent."
Vince Cable has attacked the Conservatives' plan to introduce a reported 50 percent minimum threshold in ballots for industrial action, accusing David Cameron's party of "undermining basic workers’ rights".
The Business Secretary said the Liberal Democrats "disagreed 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 percent 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?"
Cable added: "The Tories will try and use today’s event as way to undermine basic workers’ rights."
David Cameron believes disruption caused by today's public sector strikes is "wrong", his official spokesman said.
Asked whether the Prime Minister felt strikes in the public sector could ever be justified, the spokesman said: "Does the Prime Minister think that people in this country - parents, commuters, users of public services - should have their routines disrupted? Of course he doesn't think it is right."
Asked for the PM's assessment of the impact of today's strikes, the spokesman responded that Cameron would say "any disruption any user of public services experiences is wrong".
A government minister has said fewer than 500,000 people are estimated to have taken part in today's public sector strike, a significantly lower number than union leaders have claimed.
Cabinet Office Minister Francis Maude, who is responsible for the Civil Service, said: "Our official estimates are that fewer than half a million took part in this strike action – well short of the inflated claims of union leaders.
"Within the Civil Service, there has been the lowest recorded turnout for a national strike," he added.
Labour leader Ed Miliband said the industrial action taken by public sector workers today was "a sign of failure on signs".
He said: "We don't support the strikes because they are a sign of failure on all sides.
"I think the Government bares a share of responsibility for another reason too; they promised low paid workers a £250 pay rise and it didn't happen, they've demonised teachers and I'm not going to demonise public sector workers."
A union has described the Cabinet Office's figures on the amount of people striking today as "laughable".
The Cabinet Office claims a fifth of civil servants - around 90,000 people - are on strike compared with a third in the last big walkout in 2011.
However, the Public and Commercial Services union dismissed the Cabinet Office's claims, saying: "No-one can trust this government to keep reliable figures, it can't even tell us what it's done with dozens of Home Office files."
Latest ITV News reports
Union leaders said they were "overwhelmed" by support after a strike by public sector workers caused widespread disruption.
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