Expanding opportunities for working-class children by broadening the school curriculum to include more sport, drama, art and music alongside core academic subjects will be top priorities for the Labour government, the new education secretary says today.

In her first newspaper interview since being appointed to the cabinet by Keir Starmer, Bridget Phillipson insists her aim is to “break the link between background and success”, and to ensure every child has the same level of opportunity, regardless of their parents’ means.

Phillipson, one of several cabinet ministers to have risen to the top of government from working-class families – in her case via state schools in the north-east – told the Observer: “I know that in my own life I defied the odds and I want those opportunities for every child.

“I want this department to be the department of opportunity for all children regardless of background – that the family you are born into, the town that you are from, doesn’t determine what you go on to achieve.”

She said it was working-class children “who most need a brilliant education” from the state, because their parents cannot afford to send them to private schools or buy them expensive tuition outside their state schools.

Phillipson reiterated Labour’s pledge to remove tax breaks for private schools, so that it could pay for new teachers in the state sector.

Her comments come as the government faces growing pressure from its own MPs and charities to show it is prepared to help the very poorest in society by scrapping the controversial two-child limit on state benefits introduced by the Tory government.

The policy, which would cost about £1.7bn or 0.14% of total government spending to ditch, according to the Child Poverty Action Group, is blamed for plunging hundreds of thousands of children in larger families into poverty, worsening the class divide.

Phillipson, who was appointed last week by Starmer to co-chair a taskforce on child poverty with the work and pensions secretary, Liz Kendall, refused to commit to ending the two-child limit, but insisted ending child poverty was one of the main reasons she had come into politics. She said all arms of government were directed at addressing child poverty through delivery of policies such as free breakfast clubs in schools, more housing and addressing economic insecurity.

Before what could be the first rebellion of Starmer’s premiership this week, when the Scottish National party will trigger a vote on the two-child limit in the Commons, Phillipson refused to guarantee that it would be abolished. But she said the new taskforce would look at the two-child limit and the effect it has had on increasing child poverty as part of its work.

“Our review will look at all of the ways that we can make sure that there are fewer children growing up in poverty,” she said. “We will look at all aspects of policy including education, social security, housing. It will look at all of the drivers.”

Last night Rosie Duffield, the Labour MP for Canterbury, increased pressure on Starmer from the backbenches, describing the cap as a “heinous piece of legislation”.

Writing in the Sunday Times, she said: “The Labour party needs to recognise that this is an issue of social cleansing, an anti-feminist and unequal piece of legislation, and scrap it in line with our previous party position since its conception.”

The Child Poverty Action Group’s chief executive, Alison Garnham, said: “With child poverty at a record high, it is welcome that government has committed to a bold and ambitious child poverty strategy. But there will be no way to deliver on that without abolishing the two-child limit, and the longer it remains in place an ever-increasing number of kids will be affected. The next budget is the obvious and necessary moment to scrap the policy and all eyes will be on government to see its next steps towards making life better for the 4.3 million kids living in poverty.”

On Friday Phillipson announced a review of the national curriculum, which she believes should be widened to include more emphasis on subjects restricted or cut back by the Tories.

“Sadly at the moment too many working-class kids are being shut out of opportunities to play sport, to get involved in music and drama and creative subjects, and I believe we can bring that together. That is what parents want and what I want.”

Phillipson promised to deliver “the biggest transformation in education that we have seen for a generation”, with emphasis on the crucial early years of children’s development. In the short term this will mean extending help for children who have difficulties with language, and delivering 3,000 more nursery places in primary schools.

The new education secretary admitted Labour’s general election campaign had at times been defensive and cautious because the prize of victory was too big to put at risk.

“We were all terrified about screwing it all up,” she said, “because there was such a weight of responsibility.”

An Opinium poll for today’s Observer shows a dramatic leap in Keir Starmer’s personal ratings since he became prime minister.

When the number of those who disapprove of his performance was subtracted from those who approve, Starmer’s rating stood at +19, compared with –1 in the last poll taken before the election.

Former prime minister Rishi Sunak has also seen his ratings climb after the Tories’ catastrophic defeat. It is at –22 having been as low as –38 before the election. Liberal Democrat leader Ed Davey has enjoyed a lift with his ratings at +8 compared with –2 in the final pre-election poll.