My dad was the first in his family to go to university. His father worked on a fishmonger’s counter. I was the first to go on my mother’s side. She left school at 15 to get a job. My dad passed his 11-plus, went to grammar school and on to university, a transformative experience that led to a career in academia and public service.

But so many of his friends in the Rhondda of the 1950s were not so lucky. They failed their 11-plus and headed off to the secondary modern, their life course set before they even entered their teens, the vast majority denied the benefits of education beyond 16.

On a different day, my dad might have failed and changed the course of his entire life. That wouldn’t have been right and we cannot return to such a two-tier system. We can’t judge the effectiveness of an education system by looking only at the winners and forgetting the people selective education didn’t select.

I went to university, too. I got there after attending a couple of ordinary comprehensive schools, Coed-y-Lan in Pontypridd and Barry Comp, which educated kids regardless of background or ability. They gave me the start I needed in life. I even met my wife at one of them.

The point is that they prove you don’t need selection to give children the opportunities they need to maximise their potential. You need good, properly resourced schools, good teachers, a rigorous curriculum and, most importantly, high expectations for everyone, not the low expectations that say that you can know by age 11 what a child has the right to aspire to and achieve.

Education can be the key to unlocking social mobility in a country that’s unequal. But if you want to maximise the role of education in raising people up, regardless of background, then bringing back selection through grammar schools, as Theresa May is proposing, is absolutely the last thing we should do.

It’s hard to think of a more backward educational step. Under my leadership, the Labour party will block any attempt by the Tories to increase selective schooling and to roll out more grammar schools.

But I won’t stop there. Grammar schools are only one part of the unequal system that gives some children opportunities that others are denied. For those who can afford it, private schools offer a head start, the chance of a top-quality education with the best facilities and resources and access to old-school-tie networks.

I’ll put the money from ending the charitable status of private schools towards re-opening Children’s Centres

It’s deeply unfair that, on top of this privilege, the government gives fee-charging schools extra tax breaks that save them millions of pounds every year, entrenching inequality by granting private schools charitable status. At the same time, the Tories are cutting support for the most disadvantaged children, making this elite perk look especially perverse.

On my watch, there will be no cautions or caveats about whether a private school is charitable or not, this wealthfare will end. Scrapping the subsidy for privileged private schools will raise hundreds of millions of pounds. And, if I’m the next Labour prime minister, I’ll put every penny of that into Sure Start, one of Labour’s proudest achievements and one of the most powerful antidotes to educational injustice.

Sure Start has it all. Through a relentless focus on early years’ care and education, it tackles multiple inequalities – that’s why the Tories hate it so much. And Theresa May is no supporter either. In 2010, she promised a “more focused” Sure Start. What she meant, of course, was a reduced Sure Start, a reversal of Labour investment and mass closure of children’s centres – 800 shut down by the Tories in just six years.

That’s 800 communities where children from disadvantaged backgrounds have had their disadvantage compounded. Where mothers and fathers have seen the ambitions of their children curtailed. And where hundreds of thousands of parents have had their living standards squeezed even further in the name of Tory austerity.

That’s why I’ll put the money from ending the charitable status of private schools towards reopening the children’s centres the Tories have callously, and carelessly, closed.

Callous, because of the effect closures have had: worse mental health for parents, worse outcomes for families and more dysfunctional relationships. And careless, because spending on Sure Start is an investment that pays for itself. An investment in our children and in the skills and productivity of the next generation of workers.

I want all children to get access to the opportunities my dad had and so many others are denied. By blocking selection in schools, by ending subsidies for private schools and by expanding Sure Start, Labour can fight many of the disadvantages that Theresa May’s Tories will entrench. With me as leader, we won’t just talk about it – we’ll do it.