Every parent wants their child to reach their full potential and flourish: my mum called me Faiza because it means “winner” in Arabic in the hope that success would be inevitable. It’s an emotion that runs deep, and one that politicians across the spectrum are keen to tap into, for ever promising to build an “aspirational” or truly “meritocratic” society where any individual can make it as long as they work hard enough.

Equality of opportunity is a phrase commonly used by our politicians, even for those too scared to talk about equality more generally. Yet for decades we’ve been moving in the wrong direction. A recent report by the Institute for Fiscal Studies (IFS) found that where you are born in the UK, and the income and wealth of your family, now matter more than ever in defining life outcomes, with social mobility at its worst in more than 50 years.

After decades of failure, it is past the time to see through the empty political promises and popular narratives that place the emphasis on the individual to succeed, rather than a system that is rigged against the least wealthy.The “dream big and you can do anything you want” soundbite may offer inspiration to some, but it will do nothing to deal with the country’s vast and widening wealth and income inequalities. Neither will a focus on education, a classic trope of the social mobility genre, which has never been and never will be a sufficient tool to bridge Britain’s class divides.

The challenge of social mobility is a stubborn one. Intergenerational mobility – the change in occupation or class from one generation to the next – declined by about 50% between the 1958 and 1970 birth cohorts. Even after New Labour investment in early years care and education, and the resulting dramatic decrease in child poverty in the 2000s, educational attainment gaps between rich and poor children born in 2000 were roughly the same as those born in 1980. Why?

Our natural inclination is to focus on where the poorest end up, but the logic of social mobility requires some to move down for others to move up. Yet the wealthiest in our society have stubbornly held on to their class position. This is evident in the findings that show surname status can persist for as many as 20 to 30 generations, or that those who go to the most elite private schools, the “Clarendon schools” (Eton, Harrow, Winchester, Rugby, Westminster, Charterhouse, Shrewsbury, Merchant Taylors’ and St Paul’s), are 94 times more likely to end up at the very top than those who go to any other school.

When the rich are able to maintain their privilege, there simply isn’t the room for others to join them at the top. The richest 1% of households in the UK have wealth of more than £3.6m, whereas the bottom 10% has £15,400 or less. Can you imagine starting a monopoly game with 230 times less than another player? Yet the multiple policy strategies proposed to tackle low social mobility over the years almost always sidestep wealth and ignore a key factor driving differences in life chances.

This is where the new IFS research is most insightful. The researchers found only around half of wealth persistence can be explained by differences in education and earnings between those with more or less wealthy parents. Instead, unearned income – namely wealth and wealth transfers, including inheritance – act as an increasing drag on social mobility. Owning your home, especially in London, where house prices have increased most in the country, sets you up for generations.

My academic colleagues and I often lament that even after the Occupy movement, Thomas Piketty’s bestselling book Capital in the Twenty-first Century, and Oxfam’s campaigning work focusing on the huge divides between rich and poor, inequality has only got worse. But this tends to be how inequality works. More wealth at the top means more power at the top. The rich capture our political, economic and social systems, block efforts for change and scare those who resist into submission. So rather than serious proposals to address our unequal society, all we are left with is the same old “education will fix it” mantra, or an emphasis on the individual to “pick themselves up by their bootstraps”.

The social mobility story has too often acted as cover for the rich, rather than as impetus for change. But the myths that it is founded upon are losing credibility by the day. Wealth inequality may not be getting the attention it deserves in the political sphere, but the mood among the public is markedly different, as plenty of people find themselves in an endless, exhausting rat race, working two jobs and still struggling to pay the bills. In response, many are waking up to the reality that they don’t get rich, or even comfortable, by simply working hard: they get rich by being born rich. The social mobility myth is dying – now we must demand an economic settlement that works for all.

• Faiza Shaheen is a visiting professor in practice at the London School of Economics, the Labour party parliamentary candidate for Chingford and Woodford Green, and the author of Know Your Place