It is 15 years since Tony Blair pledged to eradicate child poverty within a generation. Last week's publication of the coalition government's latest child poverty strategy reminds us just how elusive this goal has been. Initially, there was a rapid fall in child poverty as more families moved into work and benefits were increased. By 2005, 700,000 children had been lifted out of poverty – nearly a quarter of all poor children, which meant the UK leapt several places in international league tables and attracted plaudits from around the world.

But then the pace of improvement slowed and from 2005 child poverty actually started to rise. Employment could no longer be relied upon as the chief route out of poverty: by then half of children in poverty had a parent in work. Yet there was insufficient public appetite for substantial increases in financial support for families.

In 2006, the then work and pensions secretary asked me to assess Labour's child poverty strategy. I was acutely aware that some topics were off limits. Naturally I was expected to limit my focus to what the Department for Work and Pensions could actually deliver and not stray into the remit of other departments. But I was also aware that I should steer clear of inequality – the government only had an explicit commitment to end child poverty.

But as I wrote in my report: "far greater changes to the distribution of wealth, earnings and opportunities in society will be necessary before child poverty is finally eradicated".

Since 2010, child poverty has continued to fall, although at around half the rate of the early Blair years. But the chief driver has not been policy. Following the financial crisis of 2008, the living standards of the middle-income families moved closer to that of some of the UK's poorest families. What's more, the £20bn cut in benefits means that child poverty is soon set to increase sharply – by an estimated 900,000 children by 2020.

Yet despite the political mudslinging, the coalition's approach to tackling child poverty is not remarkably different from Labour's. Help with finding work and benefit payments are still the main elements, though both are being scaled back.

Just as Labour's was, the coalition's strategy is patently insufficient to eradicate child poverty. There is simply no desire to square up to the most significant barrier to eradicating child poverty: deeply unequal power, opportunities and rewards in society. Until a government strategy is prepared to focus its attention on these, when it comes to eradicating child poverty we will simply be dabbling at the edges.

• Lisa Harker was an independent adviser to the Labour government on child poverty and author of the report Delivering on child poverty: what would it take?