The Labour leadership contest has so far proved to be both inward-looking and dull. Major policy debates have been muted, and differences in opinion have been few and far between. Yet the challenge we face to both realise our values and restore confidence in the Labour Party are hugely testing and hideously complex. The current level of debate is neither an interesting nor useful place for the party to be.

The challenges created by growing inequality and stagnating social mobility are issues that should be central to our discussion. They should play a key part in the debate about our future direction. Over the last two months, letters have landed on the doormats of young people across the country aspiring to go to Oxford and Cambridge. That includes young people in my own constituency. In the London Borough of Barking and Dagenham, the letters tell a compelling story of the continuing inequality communities like mine face.

Only 62 students felt able to apply for a place at our leading universities, and only 12 were offered a place. It’s a pathetic improvement on last year’s figures, when 45 young people applied and 11 were offered a place. To put that into perspective, Eton College, with 1,300 children on their school roll, ships off between 80 to 100 students to Oxford and Cambridge every year. Dagenham Park School in our borough has a similar number of students on their school roll. But this year only one young person applied to Oxford and Cambridge from this state school and they were rejected.

The inequality goes beyond access to Oxford and Cambridge and pervades the entire higher education system. The Institute for Fiscal Studies’ latest figures revealed that while 61% of those in the highest socio-economic quintile go to university, only 19% of those in the lowest socio-economic quintile secure a university place. And while 28.2% of those in the highest socio-economic quintile who go to university get into a top university, only 2.9% of those in the lowest socio-economic quintile go to a top university.

Yet all the Labour leadership candidates appear to be in total agreement in their approach to higher education. Support for making the abolition of tuition fees Labour’s headline policy has been unanimous. But this completely misunderstands the problem we face. Social mobility has frozen and for too many poor people the system is not working. This is where Labour’s attention should be.

Our ambition ought to be to equalise life chances and the belief that abolishing tuition fees will further that aim is mistaken. The policy is not politically salient, it lacks financially credibility and it does not help us to promote greater equality. Indeed, one could argue that it is simply an open bribe to the middle classes who would benefit most from the abolition of fees, because middle class children are more likely to go to university in the first place.

The annual extra cost of this policy exceeds £9bn. Just think what that money could buy if we were to invest it in high quality early years services. Early intervention with highly qualified and well-paid staff would completely transform children’s life chances and give young people the opportunity to really develop their potential. That, more than abolishing all tuition fees, would radically change the stark statistics of inequality that the university figures expose.

Barking and Dagenham is both a working-class and a diverse borough; we only have state schools serving our community. Here, young people’s experience in their secondary schools is utterly central to their future prospects. Investing in these schools would do more to get more young people into university than subsidising the fees of young people who may well have attended a private school.

The reasons why working-class and BAME students are underrepresented at Britain’s top universities are complex and structural. That’s why it is essential that the Labour leadership contenders engage in a more substantive debate. There are plenty of ideas that experts have put forward, and these could have a substantial impact in boosting social mobility.

We need to challenge the prejudices and culture of elite institutions. And the data shows that there is huge variation between institutions as well. Why does Mansfield College in Oxford manage to recruit over 90% of its undergraduate students from state schools, whereas Trinity College lags behind with over half of its students coming from private schools? What do those figures tell us about how exclusive many institutions still are? Especially when the research evidence tells us that young people from state schools outperform those educated privately during their time at Oxford.

Why not partner schools in deprived areas with the top colleges and then have a small quota of reserved places available to the best pupils from the school if they meet the entry requirements? Why not link funding with how successful universities are at recruiting students from deprived and diverse background? Why not provide funds to stimulate better partnerships between schools and universities, so that the two sectors stop blaming each other and start working together in partnership to get more kids from deprived areas into our top universities? Joint working, shared teaching and a collaborative approach might be transformative.

The Sutton Trust has recommended heavily reducing tuition fees for the poorest students, and I agree. Focusing financial support on those who need it most by reintroducing means tested maintenance grants also makes sense. It would be a targeted, fairer and more cost-effective way of making the finances of university manageable for struggling families.

Tackling the absence of social mobility at Britain’s top universities should be a priority for any truly progressive Labour politician. Simply reiterating the strapline pledge to ‘abolish all tuition fees’ is both ineffective and unaffordable. We need a bolder, braver and more radical approach from all our leadership candidates if they want to reach beyond the party members and genuinely confront the inequality that pervades British society in 2020.