“When it comes to opportunity, we won’t entrench the advantages of the fortunate few,” promised Theresa May in her now-infamous “burning injustices” speech in July 2016. But although the Tories like to talk about social mobility, this government’s record is woeful.

The privileged have become more wealthy, while people from disadvantaged backgrounds have had their opportunities to get on and move up closed off. That’s the Tory way. Tax cuts for big business and the super-rich as one in three children grows up in poverty.

A hungry child can’t learn as well as their classmates, which is why poorer children are falling behind their peers by the age of five and this trend widens throughout primary school. A teenager who can’t afford soaring university tuition fees and skyrocketing debts has their life chances cut off at 18, with children from better-off backgrounds almost twice as likely to go to university than children from low-income families. Just this week the Resolution Foundation warned that sky-high rents are pricing young people out of moving to cities where they could earn a higher salary and learn more skills.

This government has failed on social mobility so badly that its own advisers walked out en masse in protest, warning that “nothing” was being done to deal with inequalities and social divisions.

We need radical, transformative solutions to address the inequality that is blighting millions of people’s lives. Instead of helping a lucky few to escape disadvantage, a Labour government will aim to abolish poverty completely and create a more equal society, raising the living standards and well-being of all.

Within this, the role of our education system is not just about helping a lucky, talented few rise to the top, but about ensuring that everyone can realise their potential. People sometimes point to me as someone who had a difficult start but got on in life as evidence that anyone can succeed on their own. But actually my life shows the exact opposite. Any success I have had is thanks to Labour governments that provided the council house, minimum wage, tax credits and Sure Start children's centre that enabled me to achieve it.

That is social justice. Not one person doing better than the people they grew up with, but all of us working together to give everyone the chance to reach their full potential. The very opposite of what the Tories believe or do.

Focusing solely on social mobility not only disregards overall levels of inequality and poverty, but it implies that only a few talented people deserve to escape what they were born into, thereby legitimising the inequality that holds millions back.

When the term meritocracy was first coined in 1958 by the sociologist Michael Young it was actually intended as a pejorative term, a satirical warning about a future society that relegates the many “to the bottom streams at the age of seven before”.

We won’t stand for a society in which only a lucky few succeed while inequality and poverty hold back millions. We will focus on social justice, not just social mobility, to build a society in which everyone can develop their talented and succeed regardless of their background.

A Labour government will do things very differently. Instead of mealy-mouthed promises about social mobility we will practice what we preach, creating a Social Justice Commission with wide-ranging powers and genuine independence to hold the next Labour government – and all future governments to account for improving social justice. The commission will advise ministers on policies that could improve social justice and carry out impact assessments on all government policy.

Each of the Tory leadership contenders are happy to pay lip service to social mobility but they are all responsible for the rampant inequality we see all around us. There is no clearer evidence that privilege begets and perpetuates privilege to the detriment of us all than the current state of the Tory party. The only way to give everyone a fair chance to reach their potential is by tackling the structural inequalities in our society – that will be our mission.