Theresa May pledged to defend the Union between Scotland and the UK as she made her first speech as Prime Minister.

The new leader said she would lead a “one nation” government as she arrived in Downing Street.

She was appointed Prime Minister after the Queen invited her to form a government.

Speaking outside No 10, May said: “Not everybody knows this but the full title of my party is the Conservative and Unionist Party and that word unionist is very important to me.

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“It means we believe in the union, the precious, precious bond between England, Scotland, Wales and Northern Ireland – but it means something else that is just as important.

“It means we believe in a union not just between the nations of the United Kingdom but between all of our citizens – every one of us – whoever we are and wherever we’re from.”

May vowed to tackle injustice, saying “the government I lead will be driven not by the interests of the privileged few”, adding: “Together we will build a better Britain”.

She said: “I have just been to Buckingham Palace where Her Majesty the Queen has asked me to form a new Government and I accepted.

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“In David Cameron I follow in the footsteps of a great modern Prime Minister.

“Under David’s leadership the government stabilised the economy, reduced the budget deficit and helped more people into work than ever before.

“But David’s true legacy is not about the economy but about social justice.

“From the introduction of same sex marriage to taking people on low wages out of income tax altogether, David Cameron has led a One Nation government and it is in that spirit that I also plan to lead.”

The new Prime Minister added: “That means fighting against the burning injustice that if you’re born poor you will die on average nine years earlier than others.

“If you’re black you are treated more harshly by the criminal justice system than if you’re white. If you’re a white working class boy you’re less likely than anybody else in Britain to go to university.

“If you’re at a state school you’re less likely to reach the top professions than if you’re educated privately. If you’re a woman you will earn less than a man.

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“If you suffer from mental health problems, there’s not enough help to hand. If you’re young you will find it harder than ever before to own your own home.

“But the mission to make Britain a country that works for everyone means more than fighting these injustices. If you’re from an ordinary working class family, life is much harder than many people in Westminster realise.”

In a direct message to voters, she added: “I know you are working around the clock, I know you are doing your best and I know that sometimes life can be a struggle.

“The government I lead will be driven not by the interests of the privileged few but by yours. We will do everything we can to give you more control over your lives.”

On the exit from the EU, May said: “We are living through an important moment in our country’s history.

“Following the referendum, we face a time of great national change. And I know because we’re Great Britain we will rise to the challenge.

“As we leave the European Union we will forge a bold new positive role for ourselves in the world and we will make Britain a country that works not for a privileged few but for every one of us.

“That will be the mission of the government I lead and together we will build a better Britain.”

May “kissed hands” with the Queen as part of the ceremonial meeting to make her the UK’s 76th Prime Minister and only the second woman to hold the office after Margaret Thatcher.

When the audience first began May, who was then still home secretary, curtseyed to the Queen, who shook her hand and smiled.

The two women stood chatting for a few moments, while the historic moment was captured by a photographer before their meeting began.

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.”

May and her husband Philip left the palace just before 6pm following a meeting that lasted just over half an hour.

Shortly before, outgoing Prime Minister David Cameron met the Queen to tender his resignation and recommend May as his successor.

Before arriving at Buckingham Palace, he made a statement outside 10 Downing Street accompanied by his family, wishing May well and calling his six years in office “the greatest honour of my life”.

He said he was “delighted that for the second time in British history the new Prime Minister will be a woman, and once again a Conservative”.

Earlier, Cameron led his final session of Prime Minister’s Questions at Westminster, where he told the House: “I was the future once.”