The coalition government says it will commission research into why workplaces are not more LGBT-friendly and work with firms to “improve equality”.

The pledge is in the new equality strategy, unveiled yesterday by equalities minister Lynne Featherstone.

It says: “We will work with business to consider the report’s recommendations and take steps to improve LGB&T equality in the workplace.”

Other aims include encouraging more lesbian, gay, bisexual and trans people to become involved in local and national politics, promoting better recording of homophobic and transphobic hate crimes and implementing the “first ever cross-government programme” for LGBT people.

An action plan specifically for trans people is to be developed next year.

The coalition said it would “proactively question 42 Commonwealth countries which retain homophobic legislation, with a particular focus on those countries which have the death penalty for homosexual acts”.

Another part of the strategy said that coalition would “work bilaterally with other European countries to overcome the legislative or policy barriers which prevent them recognising UK civil partnerships”.

Last week, the new head of the Tory party in Europe came under fire for trying to block a motion to call for recognition of civil partnerships across Europe.

Martin Callanan argued that the issue was a matter of states’ sovereignty but Labour MEPs accused him of trying to block equality efforts.

The strategy does not mention marriage but says the coalition is talking to religious groups and gay groups about “what the next stage should be for civil partnerships” and the possibility of religious civil partnership ceremonies.

During the pre-election period, Liberal Democrat leader Nick Clegg said he supported gay marriage, while Tory leader David Cameron said he would consider the arguments for it.

As home secretary Theresa May said last month, the coalition says it work with organisations with a “proven track record of tackling prejudice-based bullying” to stop anti-gay harassment in schools and will work with sport governing bodies to address homophobia in football.

Finally, the document reaffirms the pledge that a provision to delete historic convictions for gay sex will be included in the upcoming Freedom Bill.