The Oasis Trust, a Christian charity which does support them, conducted the poll of more than 1,300 people.
It also found believers were almost evenly split on whether gay relationships are sinful or not, with 49.6% believing "people in same-sex relationships should be fully embraced and encouraged" and 50.4% saying "being in a same-sex relationship should bring with it some bar or sanction to full participation in church life."
One per cent of those surveyed believed gay people who practice their sexuality shouldn't be allowed to go to church.
The survey also found more than two thirds of Christians (68%) said their views about homosexuality had become "more inclusive" in the past decade.
Steve Chalke, founder of the Oasis Trust, told Premier: "I think it should come as no shock. You've just got to look at what happened me when I stood up [in support of same-sex relationships].
"Lots of people stopped funding us, people stopped inviting me to things.
"There's a general fear. Everybody's scared of somebody else inside the tent.
"Privately, dozens of Christian leaders - very prominent Christian leaders - have told me that they agreed [with same-sex relationships].
Steve Clifford is the General Director of the Evangelical Alliance which has spoken up for the traditional biblical view of marriage.
Speaking to Premier in response to the survey, he said: "I think it's a shame if people are feeling that but I don't know actually how true that really is.
"I recently was in a meeting with church leaders from across the UK that hold a historically biblical orthodox view on this subject. [There was] passion in the room to be talking about this subject and for those living with same sex attraction, to be welcoming, to be grace filled, to be including!"
Listen to Steve Chalke speaking to Premier's Aaron James:
Listen to Steve Clifford speaking to Premier's Marcus Jones:
