A new pressure group has been formed within the Church of England to argue for the "full participation" of lesbian, gay, bisexual, transgender and intersex people in the life of the Church.

The aims of LGBTI Mission, whose supporters include heterosexual as well as LGBTI people, include ensuring that all LGBTI people should be "welcomed and affirmed by the Church of England", that "life-long, faithful, stable same-sex relationships, and the relationships of those who undergo gender transition, should be celebrated by the Church of England" and that the ministries of LGBTI people should be "recognised and authorised".

Among the group's objectives are "ensuring that LGBTI people are never denied access to baptism, confirmation, Holy Communion and funerals, as well as allowing those in same-sex marriages to become clergy".

Among LGBTI Mission's supporters are Bishop Alan Wilson, Rev Canon Steven Saxby and Vicky Beeching. Its chair, Simon Sarmiento, said: "We believe that now is the time for the Church of England to practise what it preaches and show love towards its LGBTI neighbours. Often an assumption is made that there is a disconnect between LGBTI people and people of faith, when in fact we know that many LGBTI people are religious, and many faith groups support LGBTI equality.

"We've seen the Church make huge strides towards equality in recent years, most notably through the 2014 legislation enabling women to become bishops, and it's now essential that LGBTI equality is similarly cemented in our institution. We know that this is what most people in the Church of England want.

"We believe that each of the asks we've outlined is achievable and, frankly, essential. We hope that others who feel passionate about equality will help and join our campaign. People are people and should be treated equally and fairly; this is a fundamental part of what the Church teaches us and it's time we took tangible steps to ensure full acceptance and affirmation of LGBTI people."

The question of how the Church of England and the Anglican Communion treated people in same-sex relationships underlay a fraught Primates meeting last month. While the leaders of the world's Anglican Churches disciplined the US Episcopal Church, which sanctions them, the Archbishop of Canterbury formally apologised for the way the Church had treated the gay community. Senior clergy and other LGBTI campaigners, including Vicky Beeching, then urged him to ensure his words were followed by actions.