Media playback is unsupported on your device Media caption The BBC's Jon Brain reports from the middle of the march in central London

Tens of thousands of people have taken part in anti-austerity demonstrations in UK cities.

The biggest march was in London, where thousands of people attended a rally outside the Bank of England before marching to the Houses of Parliament.

Union leaders and celebrities including Russell Brand and Charlotte Church have addressed crowds, while protests also took place in Liverpool and Glasgow.

The government says austerity measures are vital to cutting the deficit.

The London rally was also addressed by Northern Ireland's Deputy First Minister Martin McGuinness, former Coronation Street actress Julie Hesmondhalgh and Labour leadership hopeful Jeremy Corbyn.

The protest was organised by protest group the People's Assembly, which said 250,000 people attended. The Met Police have not estimated how many people were there.

Thousands of people also attended the rally in Glasgow, organised by Scotland United Against Austerity.

Image caption Tens of thousands of protesters gathered in Parliament Square

Image copyright PA Image caption Comedian Russell Brand addressed crowds in London's Parliament Square

At the scene

Image copyright Getty Images Image caption The march began after a rally near the Bank of England

Lauren Turner, BBC News

One of the organisers promised a "festival atmosphere" before the demonstration got under way.

And with the banging of drums and the sound of cheers resounding around the heart of London's financial district, it looked like he was right.

It you looked closely at the placards, banners and T-shirts, you saw that the issues people were shouting about were many and varied.

Homes not Trident. Save Our NHS. A living wage for mothers. Frack-free world.

One simply read: "We're mad as hell and we're not taking it any more."

Coaches from all corners of the UK had set off in the early hours, carrying some seasoned protesters and some who had felt moved to demonstrate for the first time.

A trio of bemused tourists emerging from the Tube on a day out, saying they had no idea about the demo, were perhaps the only ones who didn't have a message to spread.

The final speaker to address the crowds in London's Parliament Square was comedian and activist Mr Brand, who said he wanted a society that was better for "all of us".

"I thought fame and fortune would make me valuable. I found out that it is empty," he said. "I am going to spend the rest of my life belonging to community, embracing community and helping in whatever way I can."

Media playback is unsupported on your device Media caption Charlotte Church said everyone deserved to have a strong public sector

Singer Ms Church said: "One aspect of this that really gets under my skin is that it's all wrapped up in a 'proud to be British' package. I'm proud to be British because of our National Health Service, the welfare system and David Bowie."

She added: "We need to win back… young minds and save ourselves from decades of yuppie rule, and the way we do that is with fresh ideas, positive messages, new theories, engaging art and more public figures sticking their heads above the parapet."

'Ideological war'

Len McCluskey, general secretary of the Unite union, said: "If they think they won the war of austerity on 7 May they'd better think again."

Sinn Fein's Mr McGuinness said he would fight "right-wing Thatcherite policies", telling crowds his party would say an "unambiguous, unqualified, uncompromising 'no' to this new Tory government".

Image copyright AFP

Image copyright Getty Images Image caption Marchers set off from the Bank of England for Westminster

Image copyright AP

Green Party MP Caroline Lucas accused Chancellor George Osborne of an "ideological war on welfare".

And Sam Fairbairn, of the People's Assembly, said the London march would be the start of "a campaign of protest, strikes, direct action and civil disobedience up and down the country".

People 'suffering' - voices from the crowd

George Penny, 18, from Cheltenham, said he was at the event because he believed the Conservative Party's policy was "fundamentally flawed".

"They're not achieving the results they said they intended to achieve. Some of my friends have been seriously adversely affected," he said, adding these included people with mental health issues who'd had benefits removed.

"People in Britain at large are suffering as a result of this government."

Three generations of one family travelled from Lancashire to protest against fracking.

Laura Nike, 47, from Colne, marched alongside her daughter, Ayla, nine, and her mother, Sue, from Barrowford.

She said: "We're against everything that's going on - this government has been cutting everything. We're here as anti-frackers because they want to use Lancashire as a guinea pig for the whole country."

John Calvert, 34, originally from Belfast but now living in Shoreditch, held a "Save our NHS" banner.

He said: "I was a sickly kid so the NHS is close to my heart. I believe it's a right we should enjoy. I think Cameron is, in effect, taking the NHS away by stealth."

Click here to read more views from protesters.

'Deepening inequality'

Earlier, Labour leadership contender Jeremy Corbyn said austerity was a "cover" for deepening inequality.

The MP told BBC Radio 4's Today programme his party had been wrong to accept the Conservatives' "cuts agenda" during the general election campaign.

"Britain has become a more unequal society, is becoming a more unequal society, and austerity is a cover for actually deepening that level of inequality," he said.

Image copyright Getty Images Image caption Protesters burned placards in central London during the demonstration

Image copyright Getty Images Image caption Police officers stepped in to put out the fire

But a Treasury spokeswoman said income inequality in the UK was lower than in 2010 because the government's "long-term plan is helping working people".

"The best way to help people across the UK is to deliver lasting economic security, which is why we're continuing to work through the plan to cut our deficit," she said.

Andy Silvester, of the Taxpayers' Alliance, said austerity "has to happen".

"You can't doubt the earnestness of the protestors out here today," he said.

"But they're talking about ending austerity. The honest truth is we need to crack on with it. We're still spending £75bn a year more than we bring in and clearly I think it's time for a spending reductions programme."

Elsewhere, Adam Memon from the Centre for Policy Studies - which was founded by former Tory PM Margaret Thatcher - said austerity was unavoidable.

"Britain is one of the fastest growing economies in the developed world. It is perfectly possible to reduce the deficit and not lead to the end of civilisation as Charlotte Church seems to suggest," he said.