Speaking outside her new home, 10 Downing Street, May delivered a message directed at the British population from all walks of life.
Referring to the recent referendum on European Union membership May said: "We are living through uncertain moments in our country's history. Following the referendum we face a time of great national change.
"And I know because this is 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 pledged to fight burning injustices saying: "We must make Britain a country that works for everyone. We believe in a union not just between the nations of the UK but between all of our citizens - every one of us.
"I have just been to Buckingham Palace where Her Majesty the Queen has asked me to form a new Government and I accepted. In David Cameron (the outgoing prime minister) 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.
"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.
"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.
"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."
May said: "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."
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