Around 400,000 people have joined a march in London to oppose the coalition government's spending cuts.

In what looks like being the largest mass protest since the anti-Iraq war march in 2003, teachers, nurses, midwives, NHS, council and other public sector workers were joined by students, pensioners and direct action supporters, bringing the centre of the capital to a standstill.

Tens of thousands of people streamed along Embankment and past police barriers in Whitehall. Feeder marches, including a protest by students which set off from the University of London in Bloomsbury, swelled the crowd, which stretched back as far as St Paul's Cathedral.

The biggest union-organised event for over 20 years saw more than 800 coaches and dozens of trains hired to bring people to London, with many unable to make the journey to the capital because of the massive demand for transport.

"I'm sure that many of our critics will try to write us off today as a minority, vested interest," said Brendan Barber, the general secretary of the Trades Union Congress, which organised the march.

"The thousands coming to London from across the country will be speaking for their communities when they call for a plan B that saves vital services, gets the jobless back to work and tackles the deficit through growth and fair tax."

Barber is expected to tell this afternoon's rally in Hyde Park that there is an alternative to the "brutal" spending cuts, which have already led to the threat of 170,000 council job losses and another 50,000 elsewhere in the public sector.

"No part of our public realm is to be protected. And don't believe it when ministers say that the NHS is safe in their hands. With over 50,000 job cuts already in the pipeline – nurses, doctors, physios, midwives – in the name of so-called efficiency savings of £20bn, the NHS as we know it is already in intensive care.

"With David Cameron talking about selling it off to any willing provider out to make a profit, the NHS is facing the gravest threat in its history. Today let us say to him: we will not let you destroy what has taken generations to build. Let's be brutally clear about these brutal cuts. They're going to cost jobs on a huge scale – adding to the misery of the 2.5 million people already on the dole."

The education secretary, Michael Gove, acknowledged the public's concerns about the planned cuts, but insisted they were necessary.

"Of course people will feel a sense of disquiet, in some cases anger, at what they see happening," Gove told BBC Radio 4's Today programme. "But the difficulty we have, as the government inheriting a terrible economic mess, is that we have to take steps to bring the public finances back into balance."

Labour politicians will join the march, and party leader, Ed Miliband, will address the rally in Hyde Park.

Dave Prentis, general secretary of the Unison union, will tell demonstrators that the government faces being wiped out in May's elections.

"Every month when a library closes, a care home shuts its doors, or services for struggling young people are withdrawn, I want them to feel the fear, and anger of the people who have come here today from every part of the UK to vent their frustration and to stand up for a fairer future."

Banks and stores in Oxford Street are being targeted by the anti-cuts group UK Uncut. There are also plans to target a secret location with a mass occupation.

Around 4,500 police officers were on duty, with the human rights group Liberty sending 100 legal observers to monitor their actions.

The senior Scotland Yard officer in charge of policing the protests, Commander Bob Broadhurst, has pledged that the controversial tactic of "kettling" protesters into a confined area will be kept to a minimum. "The issues will be with the fracture groups who might want to spoil the party," he said.