Rishi Sunak has vowed to limit the impact of rising inflation on people with mortgages, as he promised to rebuild trust in the government. The prime minister said inflation was the “number one enemy” and that he was doing everything he could to “grip” the issue. Sunak told the Times he understood the concerns of families now facing crippling rises in their monthly mortgage bills, after the Bank of England increased base interest rates by 0.75 percentage points to 3% – their highest level in 15 years. “I absolutely recognise the anxiety that people have about mortgages. It’s one of the biggest bills people have,” he said. “So what I want to say to people is that I’m going to do absolutely everything I can to grip this problem, to limit the rise in those mortgage rates. “I think inflation is the number one enemy, as Margaret Thatcher rightly said. Inflation has the biggest impact on those with the lowest incomes. I want to get a grip of inflation.” The Bank of England was forced to put up interest rates to curb rising prices and warned on Thursday that the country was facing its longest recession in a century. With an estimated £50bn black hole in the public finances, Sunak said it was important that the government was honest with voters about the “trade-offs” the country faced in the chancellor Jeremy Hunt’s forthcoming autumn statement. “Everyone appreciates that the government cannot do everything. How does government do everything? It just does it by borrowing money, which ultimately leads to, as we saw, high inflation, a loss of credibility, spiking interest rates,” he said. Among the measures Sunak and Hunt are considering to address the deficit are a further two-year freeze on the lifetime pension allowance and the imposition for the first time of VAT on electric vehicles, the Daily Telegraph reported. Sunak acknowledged that after Liz Truss’s calamitous tenure in No 10, the Conservatives urgently needed to rebuild the trust of the public. He pointed to his own record as chancellor – when he introduced the Covid furlough scheme – as to why people should trust him when it comes to running the economy. “I completely acknowledge that trust has been damaged over the past few weeks and months. I realise that trust is not given, trust is earned. My job is to regain people’s trust,” he said. “The only thing that people will take away from the summer – hopefully from my track record as chancellor – I’m someone they can trust understands the economy. I’m someone they can have confidence in, who will manage us through what will be a difficult economic time. I’ve got a track record in doing it.” Apart from the autumn statement, Sunak said the main issue preoccupying him over the preceding 48 hours had been the immigration crisis in the Channel. He defended the home secretary Suella Braverman’s controversial claim that the south coast was facing an “invasion” of migrants – although he did not use the word himself. “What Suella was doing was conveying a sense of scale of the challenge we face, which is serious and unprecedented. There is no easy overnight fix to that challenge. But people should know that I’m very committed to addressing it,” he said. He also revealed that he was in a TGI Friday’s in Teesside when he learned that Truss was resigning. He said: “In one sense I had moved on, I was thinking about what was next for me. I was getting stuck into that.” But he said he felt he had a “responsibility and a duty” to stand, after discussing it with his wife, Akshata Murty. He also said he told Boris Johnson he would not run on a joint ticket with him, saying: “I was very clear with him about the fact I had strong support from colleagues in parliament and I thought I was the best person to do the job.”