The special YouGov survey suggested that 45% of Church of England followers thought same-sex marriage was right, versus 37% who believed it wrong.
It questioned 6,276 British adults - 1,523 living in England and have a Church of England, Anglican or Episcopal affiliation.
It showed support was higher among younger Christians, with around half of under 55s and three in four of those aged 25 to 34 being in favour of same-sex unions.
Anglican men over 55 were least likely to approve, with just 24% giving their approval, and half of women declared their support.
Jayne Ozanne, a leading gay evangelical Anglican and member of the General Synod, the Church of England's ruling body, said the results demonstrated that the Church of England was "out of step" with its members.
As it stands the Church's official position is that marriage is between a man and a woman.
Earlier this month the US Episcopal branch of the Anglican Communion was sanctioned by the faith's leaders over its stance on the issue.
Speaking at the Primates meeting the Archbishop of Canterbury, Justin Welby, added that the church could look out of touch in the USA and UK but stressed it was a global church and had to represent the views of 165 countries.
During the talks the Church stressed that, despite the removal of The Episcopal Church for a three year period, the church is stable and stands together.
This poll reflects the view of the general public; 56% said they backed gay and lesbian marriage compared with 27% who opposed it.
This research marks an increase on a similar poll three years ago, which found support among Anglicans to be much lower.
Jayne Ozanne, who commissioned the it, said: "These figures confirm what many of us have known for some time - that the Church of England leadership is seriously out of step with its members, and even more so with society at large.
"Far more Anglicans now believe that same-sex marriage is right than those who think it is wrong.
"It is deeply worrying that the one group that appears less open to change than any other is Anglican men over the age of 55, who are the least likely to approve of same-sex marriage. Unfortunately, this is exactly the profile of those in the senior positions of power and influence power within the Church."
The Archbishop of Canterbury opened the Primates meeting in January by making a personal apology to LGBTI Christians.
He said that he finds it a "constant source of deep sadness that people are persecuted for their sexuality."
He said he wanted to express "how sorry I am" for any pain the church has caused and still causes today.
Listen to Premier's Hannah Tooley speak to Mike Davidson from Core Issues Trust here:
