The study of some of the difficulties facing LGBT people living in the UK also revealed that 2% had undergone conversion therapy with a further 5% having been offered it.
Ministers are expected to roll-out a series of legislative and non-legislative changes to end the practice, which is used by some religious groups.
It was also revealed that 68% of same sex couples said they did not hold hands in public for fear of abuse.
Ministers’ 75-step action plan has also pledged to work with the police to improve how hate crime incidents are responded to, while greater support will be given to teachers and pupils at schools and other education bodies.
It will also see the beginning of a consultation on whether laws should be changed to make it easier for transgender people to change their birth certificates.
On launching the plan, Mrs May said it sets out “concrete steps” to “deliver real and lasting change across society”.
“I was struck by just how many respondents said they cannot be open about their sexual orientation or avoid holding hands with their partner in public for fear of a negative reaction,” she said.
“No one should ever have to hide who they are or who they love.
“We can be proud that the UK is a world leader in advancing LGBT+ rights, but the overwhelming response to our survey has shone a light on the many areas where we can improve the lives of LGBT+ people.”
Labour’s Shadow Women and Equalities Minister, Dawn Butler, said: “Much of this plan is yet more reviews and consultations.
“After years of empty rhetoric and broken promises, we need to see concrete actions to show the Government is serious about tackling the inequalities faced by LGBT+ communities.”