More than 43,000 people have joined a Facebook group that calls on the prime minister David Cameron to relieve Theresa May of her job as equality minister.

Mrs May, who is also home secretary, has consistently voted against LGBT rights and voted against the 2007 Sexual Orientation regulations that she has the responsibility of implementing.

The group, titled ‘Sack New Homophobic Equality Minister’, was formed after PinkNews.co.uk published analysis of Mrs May’s voting record on gay rights.

In 1998 she voted against equalising the age of consent and in 2000, she voted against the repeal of Section 28, legislation that banned the ‘promotion’ of homosexuality by local government and schools.

In 2001 and 2002 she voted against gay couples jointly adopting children.

In 2004, like much of the Conservative front bench, Mrs May did vote in favour of civil partnerships.

But in the same year, she did not attend parliament for any of the four votes that led to the Gender Recognition Act.

Mrs May did not attend the vote for the Equality Act (Sexual Orientation) Regulations that outlawed discrimination on the basis of sexuality for the provision of goods and services including adoption. This is a key piece of legislation that she has the responsibility for administering.

In 2008 she voted in favour of a defeated bill which said that IVF rights should require a male role model – effectively discriminating against lesbian fertility rights.

The Facebook group links to a petition signed by almost 15,000 people calling on David Cameron to strip Mrs May of the equalities portfolio, but not to sack her as home secretary. The Downing Street e-Petitions service is currently suspended so it is not possible to petition the prime minister directly.

Former prime minister Tony Blair was criticised when he appointed Ruth Kelly as minister for equality after PinkNews.co.uk exposed the fact that she had never voted for gay rights.

However, unlike Mrs May, Mrs Kelly never actually voted against LGBT rights, instead she simply absented herself from the House of Commons.

Mrs May told Channel 4 News last week: “Certainly there were some votes I wasn’t present for. But what we intend to do in government is taking forward an agenda on equalities across the whole range of equalities.”

All the main parties promised action against homophobic bullying in various interviews with the pink press in the lead-up to the election.

Mrs May said: “In this particular issue we have some very real commitments, for example in terms of homophobic bullying in schools.

“Headteachers do need, I think, to be given greater support in identifying that and dealing with that issue.”

Last week, , David Cameron appointed Liberal Democrat MP Lynne Featherstone as junior equalities minister.

Since being elected in 2005, she has a good gay rights voting record and is one of the few MPs to have explicitly championed trans rights. She held the equalities brief for the Lib Dems in the last parliament and her appointment was widely praised.