The Archbishop of Canterbury has used an address to the Trade Union Congress to make an impassioned plea for economic justice for vulnerable and disadvantaged people.

Beginning with an appeal to the Magnificat, Mary's song at the beginning of Luke's Gospel that speaks of God 'scattering the proud' and 'filling the hungry with good things' – words that drew a ripple of applause – he said the Bible is 'political from one end to the other', though 'we step into dangerous territory when either the left or the right claim God is wholly on their side'.

He called for an end to the rollout of Universal Credit, saying it was leaving people poorer, and hit out at tax-avoiding large companies and the inflated salaries of chief executives. 

He warned of the toxic nature of the divisions in modern society, saying: 'Where inequality and profound injustice seem entrenched, insurmountable, it leads to instability in our society: divisions between people, and vulnerability to the populism that stirs hatred between different ethnicities and religious groups, the rise of ancient demons of racism, antisemitism, Islamophobia and xenophobia. And the rise of extremism.'

He spoke of the rise of antisemitism and of the 'anxiety' from his Jewish and Muslim friends about the language they heard used about them. 'That is an anxiety I share,' he said. 'From the left and the right, we have seen language that is insensitive to those who have too often been talked about and less often talked with.'

When any vulnerable group is trolled on social media, he said, 'we are all diminished'.

He drew applause when he quoted Martin Niemoller's famous lines during the rise of Nazism beginning, 'First they came for the socialists and I did not speak up because I was not a socialist.'

Using words from the prophet Amos as a recurring theme – 'let justice roll down like waters and righteousness like an ever-flowing stream' – Welby called on this and future governments to put his Church's foodbanks and night shelters out of business.

'Five years ago, I said to the chief executive of Wonga that I wanted credit unions to compete him out of business,' he said. 'Well, he's gone.

'Today I dream that governments, now and in the future, put church-run food banks out of business. I dream of empty night shelters. I dream of debt advice charities without clients. When justice rolls down like waters and righteousness like an ever-flowing stream, the food banks close, the night shelters are empty, families and households are hopeful of better lives for themselves and their children, money is not a tyrant, and justice is seen.'

He hit out at levels of household debt, noting that households were now more indebted than they were in 2008 before the financial crash.

That is the result of low pay, an economy that allocates rewards through power, not for labour,' he said. He referred to the work of Bradford-based debt support charity Christians Against Poverty, who were seeing more and more people caught in debt slavery. 'More than that, when these charities help them, strengthening their families, working with them to negotiate with their lenders, it has been the understanding that the creditors would contribute so that the charity can help people get their life back on track. A full third of lenders and debt collectors simply fail to contribute. That is not an economic failure of the market, it is a failure of common human decency and values.'

His fiercest criticism was levelled at large companies that avoided paying tax.

'Not paying taxes speaks of the absence of commitment to our shared humanity, to solidarity and justice. If you earn money from a community, you should pay your share of tax to that community,' he said.

'I was in business, and I know that, within limits, its right and proper for people to arrange their tax affairs, and for companies to do so. But when vast companies like Amazon, and other online traders, the new industries, can get away with paying almost nothing in tax, there is something wrong with the tax system. They don't pay a real living wage, so the tax payer must support their workers with benefits.

'And having leached off the tax payer once they don't pay for our defence, for security, for stability, for justice, for health, for equality, for education. Then they complain of an undertrained work force, from the education they have not paid for, and pay almost nothing for apprenticeships. Those are only a fraction of the costs of aggressive tax management.'

In comments that will infuriate libertarians, Welby said unions were vital for economic and social justice: 'There must be Unions in the gig economy. There must be unions in industries being automated, unions wherever workers are vulnerable. There must be a new unionisation, or, President, there will only be a new victimisation.'

He excoriated the pay differentials between workers and chief executives, pointing out that while for those at lower income levels real earning were virtually the same as they were 20 years ago and lower by seven per cent than they were at the financial crash, but that FTSE 100 chief executives' remuneration had risen by 11 per cent over the last 12months alone. 'We need genuine living wages that enable people to save more than 10 pounds a month, if they're lucky, and put an end to the days when replacing a fridge or a car tyre is a household crisis. Unions are crucial to achieving real living wages.'

He said only a partnership between governments, civil society – including unions and churches – business and community could ' heal the sicknesses of society now and in the future'.

In questions following his address he confirmed that he wanted to see a minimum wage as set by the Living Wage Foundation – £10.20 in London and £8.75 in the rest of the UK. Noting that he and his family had been reliant on the benefit system when their children were younger, he said: 'There should be a real living wage, enough to live on and live decently.'

He said he would encourage everyone to join a trade union, including clergy.

Asked about the troubled Universal Credit system, he said: 'It was supposed to reform the benefit system, to make it simpler and more efficient. It has not done that. It has left too many people worse off than they were.' More people were left at heightened risk of hunger, debt, rent arrears and needing to use foodbanks, he said. 'What's clear is that if they can't get it right they need to stop rolling it out.'

His address had been trailed with an interview in which he stressed the importance of trade unions as 'one of the civil society institutions essential to the aim of solidarity, the common good and fully valuing all people regardless of differences in nature and capacity'.

Asked how unions should address declining membership and make themselves relevant to new generations, he replied in terms that would also resonate for the church. He said: 'I would say return to your founding values frequently. What are you here to do? But don't be afraid to change the strategy. How effective are you being? Like us, you also have to let new generations come in and shape the way you do things.'

A spokesperson from Amazon said later: 'We pay all taxes required in the UK and every country where we operate' and that the company offered employees a comprehensive benefits package and had invested heavily in Britain. 

Last week Welby had been attacked in right-wing media for his co-authorship of a report by the Institute for Public Policy Research which called for higher taxes and a reformation of the economy to serve working people better. In an article for the Daily Mail he said bluntly: 'I do not believe we can continue with an economy that works so badly for so many.'

In advance of his address to the TUC, Justin Welby tweeted a link to an article he wrote for the Huffington Post in March with the comment, 'I'm often told that Archbishops should "stick to religious and spiritual matters" and "stay out of politics".

I have a feeling today might be another one of those days, so I'm just going to leave this here.'

In his article, entitled 'Is mixing faith and politics worth the risk?' he notes that five of his predecessors have died violently, three because they were involved in politics – including St Thomas Beckett. However, he continued: 'Jesus was highly political. He told the rich that, unlike the poor who were blessed, they would face woes. He criticised the King as a fox. He spoke harsh words to leaders of the nations when they were uncaring of the needy.

'He did this because God cares for those in need and expects those who claim to act in his name to do the same. That means action – and words.'

He referred to the part the church played after 1945 in 're-imagining Britain' – the title of his book – and urged the need for the church take part in forming Britain's values today.