An open letter is signed by 14 gay and lesbian clergy, along with other members of the laity calling for "diversity" of beliefs within the church.
The church forbids marriage between same-sex partners, and will not carry out gay marriage services for the public.
Any clergy who has a gay wedding faces being defrocked.
The campaigners also claim that 11 serving bishops are gay, a number which includes the Bishop of Grantham Nicholas Chamberlain, who this week became the first in the Church of England to publicly reveal he is in a same-sex relationship.
In their letter to the College of Bishops, the group of married gay clergy and lay members called for individual parishes to have the freedom to choose whether to celebrate same-sex marriages.
It said: "We encourage you to be bold ... to what you know to be increasingly the direction of travel, not just in our church but in many churches in this country."
And in their letter to the Sunday Times they called on the college to "move away from the harm and hurt that has so often been done in the name of the church".
They wrote: "We will be praying for the College of Bishops as it meets this month. We appreciate the time may not yet be right for a change in the church's official understanding of marriage, but it is time to respect that a diversity of theology within the church now exists and many in our parishes have already made the move."
"We hope for an outcome that will enable those who wish to do so to celebrate publicly where we see God at work in the lives of our congregations without fear and in openness."
The signatories, who include Rev Andrew Foreshew-Cain, the first working CofE vicar to marry his same-sex partner in June 2014, called on the college to find a way forward that offers "greater inclusion", saying: "We will always want to see the full acceptance of lesbian, gay, bisexual, transgender and intersex people in the church."
Pressure group Changing Attitude, which campaigns to change the Anglican approach to sexuality, said the church was a long way from acceptance over same-sex marriage.
Founder Reverend Colin Coward said there was a problem for bishops who are gay and have partners.
He told the Sunday Times: "To my knowledge, there are at least 10 other bishops in the church who are gay, many of whom are in some kind of relationship."
In response to the letter a Church of England spokesman said: "The agenda for the meeting of the College of Bishops has not been published.
"Following the shared conversations process of the past two years, which directly involved thousands of members of the church, the Bishops will have an opportunity to discuss the next steps over the coming months."
Addressing the letter, a Church of England spokesman said: "The agenda for the meeting of the College of Bishops has not been published.
"Following the shared conversations process of the past two years, which directly involved thousands of members of the church, the Bishops will have an opportunity to discuss the next steps over the coming months."
The Church also criticised the speculation over other gay bishops.
The spokesman said: "Such comments should rightly be dismissed as idle speculation.
"It is surprising that campaign groups which claim to support LGBTI Christians would indulge in such irresponsible tactics whereby such claims may lead to attempts to identify individual bishops."
