Speaking outside Number 10, the former chancellor praised his predecessor’s “restlessness” and her “noble aim” to improve economic growth in the UK.

But, he added: “Some mistakes were made, not born of ill will or bad intentions – quite the opposite in fact – but mistakes none the less.”

New PM – latest updates from Downing Street

After walking up Downing Street with no supporters present, and with a serious face, Mr Sunak reiterated his comments from yesterday, saying the country was “facing a profound economic crisis” and there were “difficult decisions” to come.

But he pledged to approach the problems with “compassion” and “to place economic stability and confidence at the heart of this government’s agenda”.

The new PM added: “The government I lead will not leave the next generation, your children and grandchildren, with a debt to settle that we were too weak to pay ourselves.”

Mr Sunak made his political comeback on Monday, being appointed as the new Conservative Party leader unopposed after former prime minister Boris Johnson decided not to run and Commons leader Penny Mordaunt dropped out at the last minute.

Winning the leadership also meant he won the keys to Number 10, making him the UK’s first British Asian and Hindu prime minister, and earlier today he was asked by the King at Buckingham Palace to form a government before officially taking power.

The newest and youngest PM in modern times will now begin appointing his top team, with all eyes on which cabinet ministers will be in and out.

Mr Sunak, pictured with King Charles, replaces Ms Truss, who had seen him off during the summer-long leadership contest to take over from Mr Johnson, but became the UK’s shortest ruling prime minister after the disaster of her tax slashing mini-budget.

Earlier, after holding a cabinet meeting for the final time, Ms Truss had an audience with the King to formally offer her resignation.

In her final speech as PM, she wished Mr Sunak “every success” adding: “I know brighter days lie ahead.”

In a speech that lasted just under six minutes, Mr Sunak praised another of his predecessors, Mr Johnson, for “his warmth and generosity of spirit”.

But he said the manifesto the Tory Party was elected on in 2019 was “not the sole property of any one individual” and he would “deliver on its promise”.

The PM pointed to pledges on the NHS, education, controlling immigration and protecting the environment, as well as giving his commitment to Ukraine, saying it was a “terrible war that must be seen successfully to its conclusions”.

However, one of his main messages was that his government would have “integrity, professionalism and accountability” as he attempted to win back the trust of the public after recent weeks.

“Trust is earned,” he said. “And I will earn yours.”

Mr Sunak said he was “not daunted” by the task, adding: “When the opportunity to serve comes along, you cannot question the moment, only your willingness.

“So I stand here before you ready to lead our country into the future, to put your needs above politics, to reach out and build a government that represents the very best traditions of my party.

“Together we can achieve incredible things. We will create a future worthy of the sacrifices so many have made and fill tomorrow, and everyday thereafter with hope.”

In his first remarks since announcing he would not seek a return to Number 10, Mr Johnson congratulated the new incumbent, calling it an “historic day”.

He tweeted: “This is the moment for every Conservative to give our new PM their full and wholehearted support.”

High profile Tories joined him in sending praise on social media, with Suella Braverman, Priti Patel and Sajid Javid among the first to celebrate the appointment.

Labour leader Sir Keir Starmer, right, also congratulated Mr Sunak on “making history as the first British Asian PM”.

But he said the Tories had “crashed the economy, with low wages, high prices and a cost of living crisis”, and he reiterated his call for an immediate general election, adding: “The public needs a fresh start and a say on Britain’s future.”

Liberal Democrat leader Sir Ed Davey echoed the sentiment, tweeting: “Rishi Sunak’s words will do nothing to reassure struggling people worried sick about the winter ahead.

“He says he wants to win the public’s trust, but refuses to trust the public with a general election.”

Scottish Conservative leader Douglas Ross, left,  said: “Rishi Sunak was frank and honest about the huge economic challenges the country faces as a result of the global cost-of-living crisis, and he didn’t try to sugar-coat the fact that tough decisions lie ahead.

“But the country – like the financial markets – can be reassured that our new Prime Minister is uniquely qualified and will work day and night to steer Scotland and the UK through this period.

“Rishi is a tried and tested leader in turbulent economic times and he made it clear he will approach the current economic challenges with the same compassion that we saw from him during the pandemic.

“What came across loud and clear from his address was that our new Prime Minister is a man of calm authority and integrity who won’t be daunted by the hurdles he faces. Rishi Sunak is a serious leader for serious times.”

Meanwhile,  Jacob Rees-Mogg, pictured above,  has left his cabinet role as business secretary after Rishi Sunak became prime minister.

The senior figure said that he had changed his mind on Mr Sunak being a “socialist” in an apparent bid to keep his job as business secretary.

But a source close to Mr Rees-Mogg said: “He knows he was very close to the previous two regimes and it didn’t seem likely he was going to be appointed in the new cabinet. He’s happy to support the prime minister from the backbenches.”