At Buckingham Palace, the official London residence of the sovereign, Mrs May arrived as Home Secretary and left as the Queen’s 13th Prime Minister.
The meeting may have been held in the private apartments of the head of state and begun formally with a curtsey from Mrs May, but the Queen warmly shook hands and smiled.
What passes between the Queen and her Prime Minister during their private meetings remains private, but it was the first of hundreds.
The two women stood chatting for a few minutes, while the historic moment was captured by a photographer before their meeting began.
Mrs May was wearing her trademark leopard print shoes.
Buckingham Palace confirmed her appointment in a statement: “The Queen received in audience the Right Honourable Theresa May MP this evening and requested her to form a new administration. 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.’’
Despite the wording of the statement, a kissing of the Queen’s hand does not actually happen, according to Buckingham Palace - it is believed a handshake takes place.
In the film The Queen, Tony Blair, played by Michael Sheen, was however depicted as carrying out the gesture on his appointment.
The meeting, which began soon after Mrs May arrived at 5.25pm, lasted just over half an hour and at some point Mrs May’s husband, Philip May, joined them.
A few minutes before Mrs May had arrived, former prime minister David Cameron and his family left.
Mr Cameron was joined by his wife Samantha and their children Nancy, Elwen and Florence.
The Queen’s equerry Wing Commander Sam Fletcher was the member of the household who greeted and said goodbye to the new and old prime ministers.
During his last audience with the Queen, Mr Cameron tendered his resignation as Prime Minister.
By convention the Queen is above party politics and does not personally choose the next prime minister, so Mr Cameron’s last duty was to advise her to invite Theresa May to form the next administration.
At some point Mr Cameron’s family was introduced to the Queen, who earlier in the day toured the new air ambulance base at Cambridge airport where her grandson the Duke of Cambridge works.
After the meeting, which is thought to have lasted around 30 minutes, the former prime minister left to return to a relatively normal life.
A few moments after he departed, Buckingham Palace issued a statement to confirm Mr Cameron had resigned.
It said: “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.”
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