Theresa May makes final speech as PM ahead of Boris Johnson's arrival at Number 10

Theresa May has left Downing Street for the final time as Prime Minister with a message to successor Boris Johnson to seek a Brexit deal.

The new Tory leader has made clear he will leave the European Union on October 31 – with or without a deal – but Mrs May said his priority must be a Brexit “that works for the whole United Kingdom”.

Mrs May was offering her resignation to the Queen, with Mr Johnson expected to have his own audience with the monarch later on Wednesday to be appointed as the new prime minister.

One of Mrs May’s final acts as Prime Minister was to receive the resignations of Philip Hammond, David Gauke and Rory Stewart from their Cabinet roles.

Her effective deputy prime minister David Lidington also announced he was standing down from the Government.

Mrs May’s farewell speech in Downing Street was interrupted by a cry of “stop Brexit” from a protester outside – in reply she joked “I think not”.

But she made clear her desire for Mr Johnson to seek a deal with Brexit, having previously warned about the risks of a no-deal departure.

Mrs May and her husband leave Downing Street

Flanked by husband Philip, she said: “I repeat my warm congratulations to Boris on winning the Conservative leadership election.

“I wish him and the Government he will lead every good fortune in the months and years ahead.

“Their successes will be our country’s successes, and I hope that they will be many.

“Their achievements will build on the work of nearly a decade of Conservative or Conservative-led government.

“During that time our economy has been restored, our public services reformed, and our values defended on the world stage.

“Of course, much remains to be done – the immediate priority being to complete our exit from the European Union in a way that works for the whole United Kingdom.

“With success in that task can come a new beginning for our country – a national renewal that can move us beyond the current impasse into the bright future the British people deserve.”

Mrs May was warmly greeted when she arrived at Buckingham Palace for her final audience as Prime Minister with the Queen.

Edward Young, the Queen’s private secretary, and Major Nana Kofi Twumasi-Ankrah, the monarch’s equerry, were waiting to welcome the outgoing premier and shook her hand as she stepped from her chauffeur-driven limousine.

She was joined by her husband Philip who also shook hands with the royal aides.

The ministerial vehicle had swept across the gravel of the palace’s quadrangle and stopped at the King’s Door entrance of the monarch’s official London residence.

As Mrs May emerged from the car a group of visitors, touring the summer opening of Buckingham Palace, gave a cheer and the politician turned and waved.

Lady Susan Hussey, one of the Queen’s ladies-in-waiting, was standing in the doorway and kissed Mrs May on both cheeks and shook hands with her husband before they were ushered inside.