London: Theresa May on Wednesday became Britain's second female Prime Minister, and declared that her government would not be led by the "interests of the privileged few" and strive to fight "burning injustice". May's appointment at the Buckingham Palace, to "kiss hands" with the Queen, as the ceremony is known, came shortly after David Cameron went to the Palace to tender his resignation, the Guardian reported. Speaking as British Prime Minister in Downing Street, May, 59, praised Cameron and said she will plan to lead in the same spirit that he did - praising his legacy on social justice. She said: "In David Cameron, I follow in the footsteps of a great modern Prime Minister." She highlighted the full name of her party was the "Conservative and Unionist party" and pledged to maintain the "precious bond" of England, Wales, Scotland and Northern Ireland, The Independent reported. "It means we believe in a Union, not just between the nations of the United Kingdom, but between all of our citizens, 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," she said. "We will do everything we can to help everyone to go as far as your talents will take you," she asserted. "The government will not be led by the interests of the privileged few, it will be you," she noted. "If you are in one of the those families I want to address you directly," The Independent quoted her as saying. "If you are in a working class family your life is much harder than many in Westminster realise," she said. She also said she wanted to tackle the inequalities in modern Britain. "As we leave the European Union, we will forge a new, bold, positive role for ourselves in the world, and we will make Britain a country that works, not for the 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," The Independent quoted her as saying. Cameron, who stepped down after the electorate rejected his pleas to vote to remain in the European Union in June referendum, had earlier congratulated May as he left 10 Downing Street for the last time with his wife and children. May swept to her party's leadership, when her final opponent, the pro-Brexit Andrea Leadsom, dropped out this week after making controversial comments about motherhood. May had served Cameron as Home Secretary throughout his six years in government. The new Prime Minister was expected to make the first senior appointments to her government on Wednesday evening, including a minister for Brexit, the Guardian added. A few minutes earlier, Cameron had ranked a stronger economy, gay marriage and free schools as the heart of his legacy in a final and emotional farewell speech in Downing Street. Standing with his family, he said being Prime Minister had been "the greatest honour of my life". "It's not been easy journey, and of course we've not got every decision right," the Guardian quoted him as saying, alongside his wife, Samantha, and children Nancy, Elwen and Florence.