Bridget Phillipson has said she is ready to take on the unions in a battle over compulsory reading tests for 13-year-olds and more extracurricular activities for all children to prevent them becoming “stuck in a doom loop of detachment” from school.

The education secretary said that teaching unions, who have argued the tests were “unnecessary and distracting”, should “really think carefully” about whether they could justify standing in the way of tackling the “shocking outcomes” that exist for many working-class children.

In an interview with the Guardian, in which she said her deputy leadership campaign was “just the beginning” of her efforts to help secure Labour a second term, Phillipson warned that one in four children overall, and one in three disadvantaged children, don’t meet required literacy standards.

In response to the curriculum and assessment review published next week, there will be a new mandatory reading test for year 8 pupils in an attempt to tackle underachievement by working-class children. Schools will also be expected to informally assess writing and maths.

There will also be a requirement on every school in England to offer core enrichment activities to all pupils in five different areas including sports, arts and culture, and also outdoor activities, civic engagement and life skills such as cooking and managing finances.

Only two-thirds of secondary school pupils took part in any extracurricular activities through school last year, despite increasing their chances of progressing to work and further education. Ofsted will consider if schools are meeting expectations in their routine inspections.

Phillipson said: “I’m on the side of children and parents and my first priority has to be the best possible outcomes for children in our country, and especially for working-class kids. They only get one chance at a good education and we cannot allow this drift to continue.

“I’d urge those who are considering opposing the introduction of such a measure [reading tests] to really think carefully about whether they can justify the shocking outcomes that we see for too many working-class kids in our country.

“We’ll deliver much stronger academic outcomes for young people. But alongside that, I do worry about young people lacking a sense of purpose and feeling stuck in this doom loop of detachment and not being able to read.”

The education secretary said she was also worried about children “lacking a sense of purpose” or feeling that they didn’t belong at school, suggesting the new requirements on heads to guarantee all pupils a wider range of extra activities would help.

“We have seen a worrying trend, particularly where it comes to young men accessing all kinds of poisonous material that’s dripped in their ears online, and the risks that come of detachment, increasing radicalisation, including through far-right extremism. I want them to feel excited about being a part of something.”

Phillipson said she would continue pushing Keir Starmer to scrap the two-child benefit cap entirely in the budget, saying the evidence was clear that it must be removed to reduce child poverty.

“We need to make the biggest possible impact that we can on child poverty numbers. We have to be fighting reelection on the basis that we’ve made significant progress on bringing down those numbers. The need to do that is urgent,” she said.

“The key test is whether by the end of the parliament there are fewer children in poverty than at the start.”

After a delay publishing a long-awaited overhaul of special educational needs provision, Phillipson said she understood the financial pressures that councils were under, but that reforming for children’s sake had to be our “starting point”.

“Parents tell me the system isn’t working quite rightly, but then worry about the shape of what’s to come. That’s why it is important we take the time to get this right and to take them with us,” she said.

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Lucy Powell (left) embraces Bridget Phillipson after Powell was announced as the new deputy leader of the Labour party. Photograph: Lucy North/PA

She also sought to reassure MPs, to avoid a repeat of the internal row that blew up welfare reforms. “It’s about children and their life chances. It’s not about how we seek to save money, and that’s why we’re investing more this year and more in every year.”

Phillipson, who lost to Lucy Powell in Labour’s deputy leadership contest after being seen as Downing Street’s candidate, said she wanted to make sure that party members’ voices were heard inside cabinet regardless.

“This is just the beginning … I’ve already put education back at the centre of national life, but now I’m going to press on and do more to make sure that members are proud to be out there campaigning for a second term,” she said.

“With so much going on in the world, it can be at times difficult to cut through the noise and reach voters, not least because after all of the volatility of politics, they just want their lives to get better.

“So while this is about the story that we tell, it has to be about showing, not just telling, and people feeling better off, seeing the difference in their communities and demonstrating the change that is being brought.”

The Houghton and Sunderland MP admitted she was frustrated that Labour was so unpopular with voters. “Of course I look at the polls and recognise the challenge that we face as a party,” she said.

“But polls are a snapshot in time. We’re in government, we can turn it around … I’d much rather be delivering that change, however tough, than carping from the sidelines.”

She warned Labour MPs against slipping back into an opposition mindset. “We can’t afford to go back to the days of luxuriating in the easy choices that come in opposition. Anyone can stand up, make a speech or hold a placard and feel good about themselves, but it doesn’t make a jot of difference to people’s lives.”

At the next election, Labour must make a positive case about what it had achieved and what it wanted to deliver in a second term, she said, as well as setting out the “clear choice” voters faced between her party and Reform.

Despite the outcome of this contest, she did not deny leadership ambitions of her own. “I‘ve got a very big job in my hands as education secretary, which I think is the very best job in a Labour government. That’s all I’m focused on.”