Keir Starmer is seeking to draw new battle lines with Liz Truss by vowing to reinstate the top rate of income tax and ploughing the ensuing billions into the NHS and other public services. The Guardian understands that Labour will set out in more detail on Monday how it would use the money raised from reversing the abolition of the 45p rate outlined by the chancellor, Kwasi Kwarteng, in Friday’s mini-budget. The shadow chancellor, Rachel Reeves, will argue at the party’s conference that investing in public services such as the NHS, schools and childcare is the only way to build the foundations of a strong economy – which she warns Truss is putting at risk. She told the Guardian: “Liz Truss and I are not that different in ages. We both went to our local state schools in the 80s and 90s. But the conclusions we’ve come to after that experience seem to be a world apart. You can’t build a strong economy without strong public services.” On the first day of the Liverpool conference, Starmer said it was “hugely divisive” of ministers to hand out a tax cut to people who were paid more than £150,000, as he pledged to reverse the scrapping of the additional rate on the highest earners. It could raise at least £2bn, and possibly much more, for public spending. The Labour leader said he would not reverse the cut to the basic tax rate from 20% to 19%, as the party wanted to “reduce the tax burden on working people”. But this put him on a collision course with Andy Burnham, the mayor of Greater Manchester, who said Labour should oppose both tax moves. Burnham said Labour should go further and reverse the cut in the basic rate as well, because “I don’t think it’s the most targeted way” of helping those struggling most during the cost of living crisis. “If you cut the 20p rate, it’s not as targeted a measure as doing other things such as supporting people who are at real risk, and those are people on universal credit,” he told Sky News’ Sophy Ridge on Sunday programme. Meanwhile, Kwarteng hinted there was “more to come” from the government on tax cuts. “We have only been here for 19 days. I want to see, over the next year, people retain more of their money,” he told BBC One’s Sunday with Laura Kuenssberg. The market’s shocked reaction to Friday’s mini-budget continued apace on Sunday night, with the pound has hit a 37-year low. Sterling fell to $1.077 in early trading when Asia-Pacific markets opened after the weekend, edging closer to parity with the US dollar. In an interview before her speech, Reeves compared and contrasted her own schooling in London with that of the new prime minister, who has faced criticism for talking down her state secondary in Leeds. The shadow chancellor said she had classes in prefab huts and there were not enough textbooks, but she received a good education because of the commitment of her teachers. “My lesson from that is not to cut public services or say the state has to get out of the way, but to say that actually to have a strong and growing economy, public services are foundational for that,” she said. “You can’t have a strong economy unless you get young people getting the skills and education you need. You can’t have a strong economy unless parents are supported through good childcare, especially mums, to get back into work. “You can’t have a strong economy unless you have an NHS that is working properly so people who are ill have an opportunity to get back into work. It felt like a budget but there was nothing in there for public services.” Reeves called on Kwarteng to deliver a full budget this autumn rather than waiting until the end of the financial year next April to set out his plans for public services. She accused the chancellor of “sitting on” draft growth forecasts from the Office for Budget Responsibility, and vowed to use all tools available, including the parliamentary humble address, to get them published. “What have they got to hide? If there wasn’t something to hide, they would have published it alongside the flimsy document they published instead,” she said. Reeves, a former Bank of England economist, said the Tories might achieve “some uptick” of growth through their plan of “throwing” £70bn at the economy, but she said Labour would hold them to their promise of 2.5% sustainable growth across the country for years. She said: “We should be expecting to be feeling the benefits of that growth next year. If their plan is that good, why not? They have set the bar at 2.5% and that’s what we intend to hold them to.” Labour supported Rishi Sunak’s plans to put up corporation tax from 19% to 25%, which would still leave the UK mid-table out of G7 countries and below France and Germany. But she has suggested reforming business rates would be a more useful policy, as it is currently paid by firms before they even make a profit. She confirmed that Labour would vote against removing the bankers’ bonus cap in the House of Commons. Reeves will also pledge that a Labour government would set up a state-owned investment fund if it wins the next general election. She will say the fund would enable the state to invest directly in projects and create a return for taxpayers by investing in national schemes such as battery factories and renewable-ready ports, as part of Labour’s mission to “build British industry”. She will argue the policy is a “real plan for the climate”, a “real plan for growth” and a “real plan for levelling up”. It would be funded by a national wealth fund, with the party’s green prosperity plan, which was announced at the last Labour conference, putting an initial £8.3bn into a central pot.