Departing Prime Minister David Cameron says he will miss "the roar of the crowd"

Credit: Dominic Lipinski/Pool/AP

Theresa May officially became the United Kingdom’s new prime minister on Wednesday, after her first meeting with Queen Elizabeth in Buckingham Palace.

“The Queen received in audience the Right Honourable Theresa May MP this evening and requested her to form a new Administration,” the Queen’s press secretary said in a statement provided to PEOPLE. “The Right Honourable Theresa May accepted Her Majesty’s offer and Kissed Hands upon her appointment as Prime Minister and First Lord of the Treasury.”

Shortly after the ceremony, May spoke outside her new residence at 10 Downing Street in London, where she pledged to create “a union between all our citizens.”

“The government I lead will be driven not by the interests of the privileged few,” May said, adding that “together we will build a better Britain.”

Earlier on Wednesday, departing Prime Minister David Cameron joked that his schedule for the rest of the day was “remarkably light” as he took his final Prime Minister Questions and prepared to tender his resignation to the Queen and hand the reins over to May.

Addressing the House of Commons for the last time as prime minister, Cameron quipped, “Other than one meeting this afternoon with Her Majesty the Queen, the diary for the rest of my day is remarkably light.”

Cameron added that he would miss “the roar of the crowd and the barbs from the opposition” but promised he would be “willing on” his fellow members of Parliament from the backbenches.

“Nothing is really impossible if you put your mind to it. After all – as I once said – I was the future once,” Cameron said, referencing his memorable words to former Prime Minister Tony Blair during Cameron’s first PMQs appearance in 2005.

The departing prime minister also paid tribute to his “amazing wife, Sam, and my lovely children” as they watched his last appearance from the public gallery.

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After Conservative MPs sent Cameron off with a standing ovation, he and his family returned to Downing Street for their final hours in the residence before Cameron headed to Buckingham Palace to give his resignation to the Queen.

“The Right Honourable David Cameron MP had an Audience of the Queen this evening and tendered his resignation as Prime Minister and First Lord of the Treasury, which Her Majesty was graciously pleased to accept,” the Queen’s press secretary said in a statement provided to PEOPLE.

As the head of state, the Queen has an important role to play in the transfer of powers from one prime minister to another.

Cameron arrived at Buckingham Palace in the Prime Ministerial car to formerly offer his resignation. He then drove away in a different one.

After Cameron’s departure, May was summoned to the palace so the Queen could invite her to form a new government. May then became the 76th prime minister of the United Kingdom, and the nation’s first female prime minister since Margaret Thatcher, who led the country from 1979 to 1990.

One of the monarch’s main duties is meeting with the prime minister on a weekly basis. Queen Elizabeth has held these regular discussions with 12 prime ministers – dating back to Winston Churchhill – during her record-breaking reign. The conversations, which cover both political and personal topics, are confidential and there are no records kept of the private meetings.