The UK should be a country where "no one feels the need to hide" who they love, Theresa May said as she promised a new action plan for lesbian, gay, bisexual and transgender (LBGT) people.
The Prime Minister said the new plan would be published this summer and would aim to tackle the "injustices" faced by the LGBT community.
She promised a consultation to understand the "limitations" of the current system of gender recognition and action to tackle discrimination "in every walk of life".
Writing in the Gay Times she said there had been a "phenomenal" response to a survey of LGBT people in Britain with over 100,000 replies, making it the largest such study in the world.
"One answer that stood out to me was how many LGBT people said they avoided being open about their sexual orientation or gender identity in public, or with their own family and friends.
"I want to help make us a country where no one feels the need to hide who they are or who they love."
She said the new action plan "will set out concrete steps the Government will take to improve lives for LGBT people in this country and address some of the injustices the community has faced".
"We've also engaged with experts to understand better the limitations of the current system of gender recognition and will soon publish a public consultation on how we best reform the process.
"Trans people still face indignities and prejudice when they deserve understanding and respect.
"There's lots to do - but the UK can be proud that we are a world leader in advancing LGBT rights."
Shadow women and equalities minister Dawn Butler said: "All this Government seems to do is make announcements about future announcements, it's just empty PR.
"Theresa May announced a consultation on the Gender Recognition Act last August, but nearly a year later it hasn't even started.
"We need to see deeds, not just words, from the Conservatives. Today marks 30 years since Thatcher's Government introduced the cruel Section 28, a grim moment in our country's history, which was defended by Theresa May.
"It was repealed by the last Labour Government in 2003, a Government which did more than any other in British history to advance LGBT+ equality. "
She promised a Labour government would make LGBT hate crimes an aggravated offence, update laws to provide greater protection for trans people and ensure that health workers and teachers have specialist training on tackling homophobic, transphobic and biphobic bullying in schools.
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