Alan Johnson and Yvette Cooper argued that the Labour government could go further on inequality at the Fabian fringe event Narrowing the Gap: Making Britain more equal in Manchester.

The fringe session was chaired by Martin Bright, the New Statesman's political editor, who opened by praising the Fabian Society's recent report 'Narrowing the Gap', saying, "the Fabian Society has done an incredible job through an unstinting determination to push the agenda on inequality".

The Fabian Society's Senior Research Fellow, Louise Bamfield, outlined some examples of existing inequalities. For example, single mothers are nine times as likely to have a stillbirth as other mothers, and children with parents in professional occupations are twice as likely to get five good GCSEs as those with parents in routine manual occupations. Bamfield stressed the necessity of government interventions in order to narrow the gap in life chances and prevent the accumulation of disadvantage at each stage of the life course. For example, one of the most important developments of recent years had been the development of the early years' agenda, recognising the importance of early interventions; what was now needed was to extend the logic of this with action to address problems which begin before conception.

Bamfield also spoke of the need for the Government and political parties to make a stronger case for narrowing the gap in life chances. She discussed the widespread tendency to use anecdotal examples of exceptional social mobility – the belief that anyone can make it if they really try – to justify blaming the poor for their own circumstances. What was needed was a revolution in empathy for those struggling to get by in poverty or disadvantage. Now was the time to start campaigning for more equal life chances and making the principled case for action to narrow the gap.

Next, Geoff Mulgan, director of the Young Foundation, outlined some new challenges in thinking about equality – policy areas that didn't figure in conventional analyses of poverty and exclusion. These included: disparities between socio-economic groups in the development of non-cognitive skills and 'soft' skills (such as communications skills or interpersonal skills); the plight of most vulnerable in the labour market, particularly asylum seekers, whose exploitation constitutes a modern form of slavery; the weakening of family structures in society and the failure of state when it tries to play a role (for example, with children in care), both of which constitute a "failure of guardianship"; the increasing prevalence in modern society of psychological disorders and needs, such as mental illness, loneliness and stress; and problems of over-consumption, such as obesity, gambling and alcohol abuse.

Some of those issues fit quite neatly into a classic 'narrowing the gap' approach – you can measure them and put them on a chart – but some of them don't, said Mulgan. So there was a need to recognise these new issues, as well as keeping up the pressure in more well-established policy agendas for tackling inequalities.

Minister for Housing and Planning, Yvette Cooper, followed by discussing inequalities in two areas: child poverty and housing. She commented it was great to see the Fabians putting so much focus on poverty and inequality and paid tribute to the Society's work on life chances. On child poverty, she cautioned against underestimating just how radical and ambitious the Government's target to eliminate child poverty is. It is a relative target, and given the rate at which overall prosperity has risen, Labour had made a very significant progress. It is shocking that child poverty trebled under the Tories, who actually took policy measures that widened the gap. That should be a reminder to anyone who thinks that the Conservatives – whether it is David Cameron or Iain Duncan-Smith – is seriously concerned about child poverty. She agreed that focussing around the early years' does offers great potential. She emphasised the success of Sure Start, although noted that the timescales over which the impact can be evaluated are necessarily long. Yvette claimed that extending the welfare state to the under-5s will turn out to be the most important thing the Labour government will have done.

Housing was also hugely important issue for equality, and an area where the Government had to go much further. Yvette observed that as a country we haven't been building enough houses for a generation, and that in London around a third of first time buyers have rely on gifts or inheritance, concluding, "I think that is deeply unfair – if we end up in a world where your chances of becoming a homeowner depend on whether your parents were homeowners before you". The answer was to build more homes – this agenda isn't about concreting over the countryside, but about giving the next generation the homes they need.

Yvette was followed by Martin Narey, Chief Executive of Barnardo's. Martin explained that Barnardo's was making child poverty an important theme of its work. He said it was hard getting people to accept there is still quite abject poverty in the UK, and endorsed the need for a campaign to generate more empathy for those living in poverty. He described the specific problems faced by various groups. The fact that there are many in-work poor is a real issue. The situation for children in care was also scandalous, with the way we bring them up "almost guaranteeing their social exclusion". And the situation for many asylum seekers was bleak, with Barnardo's staff routinely handing out food parcels to them; "What happens to the Labour Party's moral compass when it enters the Home Office?", Narey asked. Narey felt that it was important to argue that Britain could afford to end child poverty, citing the recent Joseph Rowntree Foundation report which assessed the cost of meeting the Government's 2010 target at an extra £5 billion a year.

Finally, Alan Johnson, Secretary of State for Education and Skills, said that Tony Crosland's The Future of Socialism had taught him that equality of opportunity was not enough, but that the left had to be concerned with a more equal distribution of rewards. He also described many of the opportunities that Labour in government had historically missed: the was nothing about a minimum wage in The Future of Socialism, and the union movement had opposed it in the 1960s and 1970s; despite the fact that British civil servants drafted the European Convention on Human Rights, we didn't write it into British law; the Butler Act had said nursery education was to be compulsory when a date was set, but it never was. This Labour Government had addressed all of these issues, to one degree or another – something of which Labour members should be proud.

Johnson insisted that tackling child poverty would always be central to Labour's agenda, and discussed some positive developments: the Child Trust Fund had great potential, and was being extended for children in care; Sure Start was being expanded across the country with new programmes to develop non-cognitive skills.

The question-and-answer session that concluded the debate touched on a variety of issues. When asked what the Government were going to do to elevate the status of Further Education, Alan Johnson praised the FE sector, describing it as "the great motor of social mobility which has been ignored for too long". The new 14-19 curriculum was going to be hugely important here, as was the expansion of apprenticeships.

Geoff Mulgan considered how to construct a coalition of public support for policies in this area? He said it was harder politically to campaign on inequality rather than simply poverty, and suggested that in the years after 1997 "more could have been done to shift the underlying culture". He also challenged the NGO community to give the Government credit when they thought it was moving in the right direction, so that their criticisms that the Government has not gone further could not be interpreted as supporting Tory claims that the Government were moving in the wrong direction.

Louise Bamfield also suggested that public stereotypes of the poor could only be changed if the Government itself stopped recast its rhetoric surrounding interventions from a punitive agenda of preventing anti-social behaviour to a positive agenda of improving the life chances of the individuals concerned.