Public sector strikes 'a damp squib', says Cameron. Reuters

The biggest display of industrial discontent in three decades ended in a propaganda war as unions and ministers traded blows over the impact, with more than six out of 10 schools shutting in England and 6,000 NHS operations cancelled across the UK, but Heathrow airport avoiding serious disruption.

Turnout became a key battleground after David Cameron labelled the walkouts a "damp squib" amid government estimates that only half the 2 million public sector workers expected by the TUC to strike had taken part.

The TUC's general secretary, Brendan Barber, hailed "huge turnouts" on an "unprecedented" day for the labour movement as tens of thousands of workers from all corners of the state sector took part in protest marches around the UK.

Francis Maude, the Cabinet Office minister, acknowledged that the strikes over pension changes had disrupted services. According to the government the impact included:

• 62% of state schools in England shutting entirely and 14% partially closing.

• The cancellation of 6,000 out of 30,000 non-urgent NHS operations.

• Walkouts by 146,000 civil servants, representing more than a quarter of the civil service.

• Some 30-40 protesters from Occupy London entering the offices of the mining giant Xstrata. There were 21 arrests in and around its offices near Trafalgar Square.

The Local Government Association said 670,000 employees were not at work with only 56% of councils counted.

However, a Cabinet Office spokesman said: "The figures we have show that turnout was ... significantly less than the unions predicted."

Trade unions representing 2.6 million workers were striking over a range of pensions changes that they claim are too drastic to be acceptable. Some are structural, including linking the retirement age to the state pension age and transferring staff to new career-average schemes. One change is viewed as a naked money grab: increasing pension contributions to £2.8bn by 2015 in a move that amounts to a pay cut for employees.

Maude said the strikes were irresponsible as he disputed union claims that talks over pension reforms had ground to a halt. But one of the main union negotiators, the GMB's Brian Strutton, said discussions on the four pension schemes – health, education, civil service and local government – had either stalled or were insubstantive. "In most of the schemes there is really nothing going on at all," he said.

Ministers are preparing to take a more conciliatory tone with unions from Thursday as they embark on a series of meetings with union leaders, according to a senior Whitehall source. "There is a feeling that we have become too polarised over the strike and the rhetoric has been ramped up," the source said. "Now is the time to tone it down and come together and get on with the real work in negotiations."

Officials and ministers will meet union negotiators at a series of meetings before Christmas to discuss pensions for workers in local government, health, education and the civil service. There will be no extra money, but there will be scope for movement over the distribution of money that has been allocated by the government. "The strike has happened, we need to put it on one side and move on," the source added.

Unions representing NHS staff accused the Department of Health of "fiddling the figures" over its claim that only 79,000 employees of hospitals, ambulance services and NHS Direct in England did not turn up for work. That was 14.5% of the workforce, much less than the 20% that the NHS had planned for, said a health department spokeswoman.

But unions claimed 400,000 NHS staff went on strike across the UK and that the total would have been even higher if some staff had not been working normally to guarantee care of emergency patients.

Amid the scramble for factual footholds, it became clear that the impact on schools was substantial. Millions of children, including Cameron's son Elwen, missed lessons as teachers took to the picket lines and as schools closed.

A higher proportion of academies opened on Wednesday compared with the state sector as a whole: 44%. Out of the first 24 free schools, 19 were open and one was partially open. Most of the free schools are newly established, with only a single year-group.

Instead of a central march, protests were staged all over the country. In London up to 30,000 joined a TUC-organised march, accompanied by blaring music, with the Madness hit One Step Beyond proving a particular favourite.

In keeping with the Metropolitan police's promise of total policing, large fold-out metal plates known as iron horses were erected at major junctions. Across London there were 75 arrests connected with the action, including 37 in Dalston, east London, on suspicion of breach of the peace before the rally.

In Manchester, shoppers and workers on their lunch break broke into spontaneous applause as the 20,000-strong demonstration made its way through the city centre. Among the sea of placards was one with photos of Cameron and George Osborne, with the caption "This is one Eton mess that's not so sweet", and another reading "Eric Pickles ate my pension" in a jibe at the communities and local government secretary.

In Birmingham, striking teacher Kate Reynolds, 33, joined the 15,000-strong vuvuzela-blowing rally with her two children, voicing her "genuine fears about my children being taught by 66-year-olds".

Bristol's German market was doing a roaring trade, packed with children off school, and with the Orchard Pig Cider stall putting on a special "Comrade" brew of mulled cider laced with vodka to warm strikers up.

A group of around 200, many wearing Father Christmas hats and calling themselves Santa Uncut, sought to deliver lumps of coal to so-called "naughty" institutions and companies.

In some areas ambulance services struggled after thousands of workers went on strike. In Leeds, there were reports that health workers from a hospital in Chapeltown, came off their picket line to help doctors and paramedics with a woman involved in a collision with a car.

Officers in the capital were called in to provide support for London Ambulance Service (LAS) which faced "severe pressure" as a consequence of the strikes.

Some 42% of London Ambulance Service's staff took part in the action and NHS London strategic health authority said the service had received 30% more 999 calls than normal. The reason for the surge in calls is not yet known. Ambulance cover in Kent, Sussex and Surrey was also "significantly hampered".

Hospitals in Merseyside, Cheshire and northern Wales were handling urgent appointments only. East Sussex Healthcare NHS trust said "no planned operations have been cancelled" but the Mid Yorkshire Hospitals NHS trust reported all planned operations cancelled, including "virtually all" outpatient clinics with a few exceptions.

The BBC's One Show apologised after the TV presenter Jeremy Clarkson suggested on air that strikers should be "executed in front of their families". Clarkson sparked outrage on Twitter after telling viewers that he would have striking public sector workers shot. "I would have them taken outside and executed in front of their families," he said.

In Edinburgh an estimated 10,000 took their protest to the Scottish Parliament after a colourful rally from Edinburgh Castle, among them A&E staff nurse Sharon Edgar, 37, from Rosyth, Fife, with her daughter Beam, eight.

She said she had thought "long and hard" before striking. "My little girl wants to be a nurse too. If we don't stand up now, what kind of deal will she get?"

At Edinburgh's Royal Infirmary, veteran trade union leader Rodney Bickerstaffe – a pivotal figure in the 1979 "winter of discontent", when 1.5 million public sector workers went on strike – joined a picket line of nurses, lab workers and cleaners.

"These are the people who work day in, day out, they wipe noses, they wipe bottoms, they teach unruly kids, work with dustbins and sewage works," he said of the public sector workers. "They are the services which civilise our society." Glasgow had another 10,000-strong rally by strikers.

In Inverness, strikers wearing Danny Alexander masks and carrying "swag bags" descended on the constituency offices of the chief secretary to the Treasury, protesting at his pensions "cash grab".

Alexander, the Lib Dem MP for Inverness, Nairn, Badenoch and Strathspey, has become the chief hate figure within the UK government for Scottish union leaders because of his government role as one of the leading pension negotiators.

For many, such as Inspector Russ Aitken from Mersey Tunnel police, it was the first time they had taken industrial action: "I feel angry that I'm paying a 50% increase in pension contributions and I feel angry that I'm going to have to work longer."

Court staff also found themselves on picket lines.

Norina O'Hare, from the justice and prosecutions sector of the PCS union, said: "We've had a lot of support from judges who are, of course, also public sector workers."

• This article was amended on 1 December 2011 to correct the name of the GMB negotiator Brian Strutton.