Rishi Sunak has said he would find up to £10bn to help people facing rising energy bills, as a minister backing his Conservative leadership rival indicated that direct support for the hard-pressed would be announced “in a considered way”. Acknowledging he would have to increase government borrowing to tackle the crisis, the former chancellor sketched out what he envisaged would be a support package for up to 16 million vulnerable people. “People need reassurance now about what we will do and I make no apology for concentrating on what matters most,” Sunak wrote in the Times, which reported that he valued a cut to VAT on energy at £5bn. He was also said to have pledged to find the same amount again to go towards helping those most in need, as he said: “You can’t heat your home with hope.” It comes after Sunak claimed Liz Truss’s cost-of-living plans could put vulnerable people at risk of “real destitution”, with economic policy once again driving a wedge between the candidates. As Sunak and Truss took to the stage for the latest Tory party hustings in Cheltenham, Sunak refused to rule out “some limited and temporary one-off borrowing as a last resort to get us through this winter”. He also said that without further direct payments, pensioners and people on very low incomes could face serious hardship. However, the work and pensions secretary, Thérèse Coffey, who is supporting Truss, hit back on Friday morning, taking a veiled swipe at Sunak for not waiting for the energy regulator Ofgem to make a key announcement about the energy price cap before his latest intervention. Defending Truss, Coffey said: “She is absolutely an MP who knowns what it is like for struggling households and that is why, quite rightly in a considered way, once Ofgem comes up with their price cap … all of government … and it will be decision for the new prime minister to enact what changes could be made.” Referring to Sunak, she said: “I appreciate what he is saying that but Ofgem has not reported. When he was chancellor he waited for Ofgem to report before coming up with some proposals.” Coffey told BBC Radio 4’s Today programme that she had delivered that previous support through legislation and at the time had been “blocked within government” when she asked for powers to make payments more quickly. “I have delivered that through legislation and at the time I asked for powers to be able to make payments more quickly. That was not given to me. That was blocked within government so if we are going to do things through the welfare system we would have to do brand new primary legislation,” she said. Sunak’s comments in Thursday’s hustings came after Truss, in her own Q&A session at the event, reiterated her belief that tax cuts should be the main response to soaring bills. Truss told the audience of Tory members that this would always be her “first port of call”, followed by a focus on longer-term energy supply issues such as support for fracking and nuclear power. Truss said she could provide other assistance, but gave no details, saying she “can’t write the chancellor’s budget” before even being elected as prime minister. “If the answer to every question is raising tax, we will choke off economic growth, and we will send ourselves to penury, and I think that’s a massive problem,” she said.