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More than two-thirds of LGBT people in the UK avoid holding hands in public due to fears about negative reactions, according to a government survey.
Results also showed LGBT people are more likely to be "less satisfied" with life than the rest of the population.
Prime Minister Theresa May said nobody "should ever to have to hide who they are or who they love".
In response to the survey, the government has produced a 75-point plan to improve the lives of LGBT people.
The charity Stonewall added there were still "pockets of society" where the LGBT community was "far from safe".
More than 100,000 people took part in the survey, which was carried out between July and October last year.
Those identifying as gay or lesbian made up 61% of respondents. Just over a quarter identified as bisexual and a small number identified as pansexual (4%) and asexual (2%).
People identifying as transgender accounted for 13% of respondents.
A quarter of those who took part in the survey said they were not open at all about being LGBT with family members they lived with.
Of the trans men who took part in the survey, 56% said they had avoided expressing their gender identity for fear of a negative reaction from others.
That figure rose to 59% for trans women and 76% for non-binary respondents.
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LGBT hate incidents had been experienced by 40% of people in the survey, with more than nine in 10 of the most serious offences going unreported.
The prime minister said the results "shone a light" on the "many areas where we can improve the lives of LGBT people".
Equalities minister Penny Mordaunt told BBC Breakfast: "There's still much more that we need to do to enable people to thrive, to access healthcare services and to ensure that they can go about their daily business without fear or feeling intimidated."
The government's new "action plan" aims to help "tackle discrimination and improve the lives of lesbian, gay, bisexual and transgender" people in the UK.
One of the commitments in the plan is to "eradicate the abhorrent practice of conversion therapy", which 5% of survey respondents said they had been offered, and a further 2% said they had experienced.
"We will consider all legislative and non-legislative options to prohibit promoting, offering or conducting conversion therapy," the plan states.
Ruth Hunt, chief executive of Stonewall, said she was pleased the government was listening to the LGBT community, but added there was "still a long way to go until we reach full equality".
Campaigner Peter Tatchell welcomed the government trying to ban conversion therapy. But he said the 75 point-plan did not go far enough.
"The biggest fail is the lack of any pledge to end the detention and deportation of LGBT+ refugees fleeing persecution in violently homophobic countries like Uganda, Iran, Russia, Egypt and Jamaica," he said.
"Another big omission is the absence of any commitment to compensate gay and bisexual men who were convicted under past anti-gay laws."
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