The new Labour leader has given his first big public address – to trade union delegates at the TUC Congress in Brighton.

He caught the eye of headline writers by insisting that the Conservatives were “poverty deniers”.

But did he pass the FactCheck test?

“We can look away from the policy of growing inequality and look to a society that grows in equality… and does not allow the gross levels of poverty and inequality to get worse in Britain.”

Does Britain really experience “gross levels of poverty and inequality”? Is inequality growing? The statistics are not all that straightforward.

There’s actually no single definitive measure of poverty or inequality.

Poverty can be “relative”, which is often defined as someone’s income falling below 60 per cent of the median average income.

This means that of average incomes fall people will be automatically “lifted out of poverty” even if their income doesn’t change. Some would argue that this is really a measure of inequality.

“Absolute poverty” is when you measure income against a fixed point. In government figures that benchmark is the median average income in 2010/11 held constant in real terms.

Then you can measure people’s income before or after housing costs are taken out of the household budget. Campaigners like the Child Poverty Action Group prefer the “after housing costs figure”.

Did poverty get worse under the coalition?

The latest official statistics suggest that rates of relative poverty fell slightly but absolutely poverty went up between 2009/10 and 2013/14:

What happened to children? Mr Corbyn said:

“Child poverty rose by half-a-million under the last government to over four million.”

This is true but doesn’t tell the whole story.

Again, the numbers of children in relative poverty actually fell under the coalition government – from 3.9 million children in 2009/10 to 3.7 million in 2013/14.

Only if you look at the absolute poverty measure do we find an increase – from 3.6 to 4.1 million children under the same period – which supports Mr Corbyn’s words today.

But the total number of children in the UK rose in those years so as a percentage of all children, the rise of children in absolute poverty is less dramatic.

These are the latest figures for four measures of child poverty used by the government, expressed as a percentage of all children.

Child poverty rates are fairly flat over the last five years we know about:

However, there is some support for the ideas that things could get worse (on some measures) in the future thanks to coalition – and now Conservative – policies.

The independent Institute for Fiscal Studies says: “Looking further ahead, planned benefit cuts over this parliament will hit low-income working-age households hardest, and will therefore tend to put upwards pressure on absolute income poverty.”

Inequality

Again, this can be measured in different ways, but the official figures do not provide very clear evidence for the idea that income inequality became markedly worse under the last government.

The IFS looks at three measures in its latest study: the Gini coefficient (a value between 0 and 1 – the higher the number, the more inequality); the ratio between the incomes of the top and bottom-earning 10 per cent; and the share of income held by the richest 1 per cent.

On all three measures, income inequality fell between 2007/08 and 2013/14, according to the IFS, although the top 1 per cent have generally been getting richer since the 1980s.

The think tank says: “The last 25 years have seen income inequality fall across most of the distribution, but the top 1 per cent of individuals have taken an increasing share of total household income.

“The common perception that inequality is rising may be based on the ‘racing away’ of a small group at the very top of the pile, rather than on trends in inequality across the vast majority of households.”

“There are six million of us in this country.”

The “us” here refers to trade unionists. The figure is absolutely correct, according to official statistics: “Around 6.4 million employees in the UK were trade union members in 2014.”

This number was down very slightly – 40,000 members – from the year before, and compares to the peak of union membership in Britain in 1979, when more than 13 million people were union members.

In 2014, exactly a quarter of workers (25 per cent) were members, the lowest rate since 1995. Membership has been growing in the private sector and falling in the public sector since 2010, reversing the previous trend.

Union membership has fallen more sharply among men than women.