The government will appoint a national LGBT health adviser and take measures to end so-called conversion therapy as part of a plan to deliver what Theresa May has promised will be “real and lasting change”.

The proposals form part of an action plan published by the Equalities Office on Tuesday. It follows a UK-wide survey of LGBT people that had more than 108,000 responses, billed as the largest study of its kind.

The 30-page plan contains a series of pledges, including to improve the police response to LGBT hate incidents, more support for LGBT students and teachers and improvements to gender identity services for transgender adults.

The proposals, which will receive an initial £4.5m in funding, were welcomed by the campaign groups Stonewall and the LGBT Foundation. Ruth Hunt, Stonewall’s chief executive, said she was “really pleased that the government is listening to the thousands upon thousands of LGBT people who responded to this survey”.

The online poll, which ran from July to October last year, sought views from LGBT and intersex people about their personal experiences and interactions with public services.

Penny Mordaunt, the minister for women and equalities, said: “Our action plan is a step towards everyone, regardless of their sexual orientation, gender identity or sex characteristics, being able to live safe, happy and healthy lives where they can be themselves without fear of discrimination.”

May is to host the annual Downing Street LGBT Pride reception on Tuesday evening. Among the guests for the first time will be Peter Tatchell. The veteran campaigner said May had invited him after he was “banned” previously.

In a separate statement, Tatchell called the action plan a “welcome start”, but said it fell short on issues such as the deportation of LGBT refugees to countries where homophobia was widespread. The £4.5m budget was “derisory and insulting”, he added.