Mrs May said she would use the next 12 months to ensure Britain negotiates the right EU withdrawal deal for people whether they voted Leave or Remain.
Acknowledging the social and economic divisions laid bare by the Brexit campaign, Mrs May said Britain needed to come together, stating: “As the fantastic MP Jo Cox, who was so tragically taken from us last year, put it: ‘We are far more united and have far more in common than that which divides us’.”
The Prime Minister said the UK is positioned to seize the “great opportunities” ahead.
“We have made a momentous decision and set ourselves on a new direction. And if 2016 was the year you voted for that change, this is the year we start to make it happen.
“I know that the referendum last June was divisive at times. I know, of course, that not everyone shared the same point of view, or voted in the same way.
“But I know too that, as we face the opportunities ahead of us, our shared interests and ambitions can bring us together.
“We all want to see a Britain that is stronger than it is today. We all want a country that is fairer so that everyone has the chance to succeed. We all want a nation that is safe and secure for our children and grandchildren.
“These ambitions unite us, so that we are no longer the 52% who voted Leave and the 48% who voted Remain, but one great union of people and nations with a proud history and a bright future.
“So, when I sit around the negotiating table in Europe this year, it will be with that in mind - the knowledge that I am there to get the right deal - not just for those who voted to Leave - but for every single person in this country,” Mrs May said.
The Prime Minister said the divisions revealed by the Brexit campaign needed to be addressed in 2017.
“Of course, the referendum laid bare some further divisions in our country - between those who are prospering, and those who are not; those who can easily buy their own home, send their children to a great school, find a secure job, and those who cannot; in short, those for whom our country works well, and those for whom it does not.
“This is the year we need to pull down these barriers that hold people back, securing a better deal at home for ordinary, working people.”
The Prime Minister said she wanted to create a country that worked for all and “not just a privileged few”.