UPDATE 3-UK's teachers and civil servants join mass strike on 'Walkout Wednesday'
Tens of thousands of teachers march in London
Prime Minister Sunak condemns strike
Government says big pay rises will fuel inflation
Schools shut, most trains not running
(Adds PM comment, education workers' rally)
By Alistair Smout and Michael Holden
LONDON, Feb 1 (Reuters) - Up to half a million British teachers, civil servants, and train drivers walked out over pay in the largest coordinated strike action for a decade on Wednesday, with unions threatening more disruption as the government digs its heels in over pay demands.
The mass walkouts across the country shut schools, halted most rail services, and forced the military to be put on standby to help with border checks on a day dubbed "Walkout Wednesday".
According to unions, as many as 300,000 teachers took part, the biggest group involved, as part of wider action by 500,000 people, the highest number since 2011, when civil servants walked out en masse.
Prime Minister Rishi Sunak condemned the strikes which forced millions of children to miss school.
"I am clear that our children's education is precious and they deserve to be in school today being taught," he said.
His government has taken a hard line against the unions, arguing that giving in to demands for large wage hikes would further fuel Britain's inflation problem.
Tens of thousands of education workers marched through central London with placards which read "Children Deserve better" and "Save our Schools, Pay Up".
Taking part in the march, primary school teacher Hannah Rice, 32, said she hoped the scale of the action would send the government a strong message.
"This government should be ashamed of the way they are managing things," she said. "It's clear people are unhappy, it's clear that there needs to be a change."
The PCS Union, representing about 100,000 striking civil servants from more than 120 government departments, warned of further co-ordinated strikes.
"If the government doesn't do something about it, I think we will see more days like today with more and more unions joining in," PCS general secretary Mark Serwotka told Reuters.
"We need money now," he added.
With inflation running at more than 10% - the highest level in four decades - Britain has seen a wave of strikes in recent months across the public and private sectors, including health and transport workers, Amazon warehouse employees and Royal Mail postal staff.
Next week, nurses, ambulance staff, paramedics, emergency call handlers and other healthcare workers are set to stage more walkouts, while firefighters this week also backed a nationwide strike.
The strikers are demanding above-inflation pay rises to cover rocketing food and energy bills that they say have left them struggling to make ends meet.
So far the economy has not taken a major hit from the industrial action, with the cost of strikes in the eight months to January estimated by the Centre for Economics and Business Research at about 1.7 billion pounds ($2.09 billion), or about 0.1% of expected GDP.
It put the estimated impact of the teachers' strikes at about 20 million pounds a day.
But the strikes may be having a political impact on Sunak's government.
His Conservative Party has been trailing the opposition Labour Party by as much as 25 percentage points in polls and surveys indicate the public think the government has handled the strikes badly.
Mary Bousted, General Secretary of National Education Union, told Reuters that teachers in her union felt they had no choice but to strike as declining pay meant high numbers were leaving the profession, making it harder for those that remain.
"There has been, over the last 12 years, a really catastrophic long term decline in their pay," she said outside a school in south London.
"They are saying, very reluctantly, that enough is enough and that things have to change."
The school closures have made life difficult for millions of working parents.
Miranda Evans, 44, a policy and programmes manager from south Wales, said she supported the strikes but they had left her working from home while also looking after her three children aged 15, nine and six.
"They're all currently around me while I'm sending emails," she said. "It's highly stressful." ($1 = 0.8130 pound)
(Reporting by Michael Holden, Alistair Smout, William Schomberg, Natalie Thomas, Will Russell, Yadarisa Shabong, Ben Makori, Gerhard May and Sarah Young; Editing by Jonathan Oatis, Raissa Kasolowsky and Christina Fincher)