The core fairness test should be 'that we should not inherit our life chances at birth', said Katwala, arguing that this 'fight against fate' should provide the lodestar to guide future action and campaigns for equality.

This would require all parties to deepen their commitments on child poverty and tackling educational inequality.

The government should hold a 2009 Comprehensive Spending Review to timetable concrete steps for spending per pupil in state schools to match that of the private sector, he argued, proposing that putting VAT on private school fees could finance a new opportunity fund to tackle educational disadvantage, he said.

Katwala challenged the myth that 'social mobility has declined under Labour' as 'just plain wrong'. It takes thirty years to measure social mobility. This was an ideologically motivated myth, to try to back up the argument that the state must fail.

Understanding why Britain and the United States have much lower mobility than Germany and the Nordic countries should lead to a deeper focus on economic inequality, early years support and educational disadvantage.

Ending child poverty should be the top priority. 'The good news is that each of the three major parties are now signed up to the goal of ending child poverty by 2020. The bad news is that none of them has policies which can achieve this', said Katwala.

He also called on leading black and Asian campaigning groups and opinion formers to do much more to campaign on child poverty: 'No other single issue will have more impact on tackling disadvantage in ethnic communities'.

'Breaking the cycle of disadvantage across generations can not be done without a sustained project for more than one political generation too', Katwala argued. This would require a new 21st century public settlement on poverty and inequality to prevent progress being reversed.

The Fabian Society and Webb Memorial Trust would be addressing this in a major project over the next two years, marking the centenary of the 1909 Minority Report on the Poor Law, which began a public debate about the collective responsibility to tackle poverty, he said.

All parties faced important challenges. Labour needed to show that it had not reached the limits of progress, by making and winning a public argument for a deeper agenda on inequality.

The Conservative Party had changed its position, accepting the argument for relative poverty. However, Katwala pointed to 'significant gaps' in Conservative social justice thinking.

'Family breakdown – like addiction and debt – are identified as important causes of poverty; but what is missing is any understanding of poverty as a potential cause of family breakdown, or addiction, or debt'.

The new LibDem leader would need to ensure his party's policies 'met the redistribution test', rather than redistributing to the middle not the bottom, and would have to show how the localism agenda could be equality-proofed.

• Sunder Katwala, General Secretary of the Fabian Society, was speaking at 'Diverse Britain 2007: Promoting Race Equality' held by The Guardian and the Equality and Human Rights Commission, Tuesday 11th December at the QEII Conference Centre, London.

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