Just 2% of fans think there are no gay professional players, the survey said
English football is "institutionally homophobic", the gay rights group Stonewall has claimed.
Its survey of 2,005 fans found 70% had heard anti-gay abuse in grounds in the past five years and more than half felt authorities did not do enough about it.
Stonewall chief executive Ben Summerskill said homophobia in football "almost always goes unchallenged".
But the Football Association said: "There is no place in the game for homophobic or racist abuse."
'Not doing enough'
The survey suggested that most fans did want to see an end to homophobia in the sport, with 64% saying football would be better off without anti-gay abuse and more than two-thirds saying they would feel comfortable if a player on their team came out.
Also, 85% supported the action taken by police against fans who directed homophobic and racist abuse at Portsmouth's Sol Campbell in October 2008.
However, while 61% believe there is less racist abuse in contemporary football compared with 1989, just 31% believed there was less homophobic abuse.
Some 63% blamed the prospect of anti-gay abuse from fans as the reason why there were no openly gay players in the Premier League, Championship and Leagues One and Two. Just 2% believed there were no gay professional players.
Only one in six fans said their club was working to tackle anti-gay abuse and 54% believed the Football Association, Premier League and Football League were not doing enough to tackle the issue.
In response to the figures, a report by Stonewall argues that clear leadership is needed from the FA and from clubs to tackle the problem.
Its recommendations include using sanctions against fans who carry out anti-gay abuse and violence similar to those who conduct racist abuse.
Clubs which fail to tackle homophobia should face the threat of points being docked, the report also says.
Taunting and bullying
Additionally, it recommends that Kick It Out, the FA's anti-abuse campaign, should be better resourced to tackle homophobia.
Mr Summerskill said too little action had been taken on an issue which deters gay and straight fans and players alike from enjoying the game.
He added: "Sadly, this survey demonstrates that football is institutionally homophobic.
"When England is looking to host and win the 2018 World Cup, football cannot risk this loss of potential talent and supporters."
Chris Basiurski, chair of the Gay Football Supporters Network, said he was "not surprised" by the report's findings.
He added: "Our own experiences show that many in the football world are in denial over the problem and have been unwilling to help us in our campaigns."
Graham Le Saux endured years of taunts
Former England star Graham Le Saux, who was repeatedly taunted after rumours wrongly labelled him as being gay, said: "The homophobic taunting and bullying left me close to walking away from football.
"I went through times that were like depression."
However, a spokesman for the FA said changes in ground regulations had made homophobic abuse punishable, and the association "calls for the strongest possible sanctions to be taken against anyone who is found guilty".
The spokesman said the FA was in "constant dialogue" with fans and had worked with police following the abuse directed at Mr Campbell.
He added: "The FA recognises that football has a duty to tackle all discrimination within the game and aims to confront aggressive issues such as homophobia."
Professional Footballers' Association chief executive Gordon Taylor said the players' union had a "zero-tolerance" policy on all forms of discrimination.
"We are working with Kick It Out and the Football Association on an anti-homophobia campaign that will tackle the issue head-on," he said.
A Premier League spokesman said: "The Premier League and all our clubs take discrimination extremely seriously and it's a standard part of all Premier League ground regulations that all abuse - be it gender, race or sexual orientation-based - will not be tolerated."
A spokesman for the Football League, which runs the Championship and Leagues One and Two, said its clubs did not tolerate abusive behaviour, adding that stewards were being trained to tackle it.
He said: "League clubs are working hard to deliver a match-day environment that is welcoming to everyone in the community."