As Gordon Brown marks his first anniversary in No 10, the prime minister will no doubt be contemplating the deterioration of Labour’s fortunes over the past nine months. One thing is for sure: he will not be short of advice on how his government can dig themselves out of the electoral hole in which they currently languish. At least some of it, however, should carry a strong political health warning.

There will be those urging Brown to begin by tending to Labour’s alienated core vote: refocusing on traditional concerns such as inequality; adopting a much more aggressive tone towards business; arguing the case for greater state intervention and calling a halt to the privatisation and marketisation which supposedly characterises the government’s approach to public service reform. The New Labour agenda will once again be dismissed as neither new nor Labour.

The prime minister needs no reminding of the dangers of such an approach. First, those who bemoan the frayed relationship between Labour and its traditional supporters would have him believe that there is a choice to be had between reconnecting with such voters and reassembling the kind of winning electoral coalition which Labour constructed in the late 1990s. But if Labour is to secure a fourth term, it must appeal to both the concerns of middle England floating voters and the working poor.

Second, implicit in the arguments of many of New Labour’s critics is a fundamentally flawed characterisation of the agenda of the past 10 years and a wilful attempt to construe its record as some kind of free market fundamentalist continuum with the governments of Margaret Thatcher and John Major. Most damagingly, they also claim that Cameron-style ‘one nation Conservatism’ may well be ‘more progressive’ than the alleged ‘market-first politics of New Labour’.

But such lazy thinking belittles the real redistributive achievements of New Labour over the past decade – achievements secured at the same time as the party was winning repeated victories at the polls. And more dangerously, it signals to voters that the outcome of the next general election does not really matter, that a Conservative or Labour government would pursue much the same agenda with many of the same results. Such a view thus takes totally at face value David Cameron’s rhetoric around arresting Britain’s ‘social recession’ and mending its ‘broken society’. In truth, there is nothing concrete in the Tories’ still largely undefined policy agenda to suggest that any of the Conservative leader’s fine words and aspirations will ever become any more than that.

By contrast, the first of our progressive challenge ‘green papers’ published this month, From Public Sector to Public Service: Putting Citizens in Control, shows the New Labour case in action: how the pursuit of further public service reform is the prerequisite for a new 21st century social justice agenda. The report thus argues (previewed on page 10) that it is not slowing up on reform that will best realise our core values, but speeding up.

Two suggestions floated by the green paper show in particular how empowering public service users and tackling inequality can be brought together.

The first proposes that parents could be given a credit to spend on childcare, made up of the childcare element of the working tax credit, the nursery education grant, and the Sure Start general grant to local authorities. But, in addition, the credit should be weighted to give more to low-income families or people in training and employment. This proposal ticks many of the traditional boxes reformers are keen to see checked – allowing greater choice and control to be exercised by individual citizens – while also containing what might be termed an ‘equality premium’, designed to ensure that those in most need of better public services gain the most from the reforms.

Second, the green paper floats giving pupils from deprived or disadvantaged backgrounds who are struggling or falling behind an education credit to be spent either in school or with an approved educational tutor. Moreover, schools should receive part of their funds according to the value they add to their pupils’ education, thus providing incentives for them to secure more socially balanced intakes.

These proposals, combined with a wider right for all parents in failing schools to choose an alternative school for their children, would ensure that schools work hard to attract students from more disadvantaged backgrounds rather than the current system which cherry-picks the brightest.

In each of these cases, reform seeks to challenge public services which too often entrench, rather than tackle, ingrained inequalities and impede, rather than further, greater social mobility. It’s an emerging agenda which offers a greater chance to realise Labour’s values than cheap shots about New Labour and warm words about David Cameron.