The study, undertaken by a cross-party parliamentary committee, found that while anti-racism schemes had proved successful, fans were becoming increasingly aware of homophobic chants at grounds.
"Evidence is now emerging that homophobia may now be a bigger problem in football than other forms of discrimination," the report said. "Recent research found that 25 per cent of fans think that football is homophobic while 10 per cent think that football is racist."
It added that 14 per cent of match attendees questioned had reported hearing homophobic abuse.
"The FA should work with relevant organisations and charities to develop and then promote a high-profile campaign to highlight the damaging effect of homophobic language and behaviour in and around football at every level," the report concluded.
"The campaign should identify sources of support for affected individuals as well as setting out a clear reporting structure for homophobic incidents."
Justin Fashanu is the only British top flight player to have announced during his professional career that he was homosexual.
He committed suicide in 1998, aged 37.
The wide-ranging report by the Department for Culture Media and Sport committee, said that while the atmosphere inside British football grounds had improved since the 1970 and 1980s, becoming more family-friendly, significant problems remained.
Two high-profile on-field cases brought racism back under the spotlight.
Chelsea captain John Terry was cleared in court of racially abusing Queens Park Rangers defender Anton Ferdinand in July while last season Liverpool's Luis Suarez was banned for eight matches by the FA for comments made to Manchester United's French defender Patrice Evra.
Terry could yet be charged by the Football Association.
Conservative parliamentarian John Whittingdale, chairman of the committee, said: "Much has been done to improve the atmosphere and behaviour at football matches and it has become a much more family friendly activity.
"However, recent incidents of racist abuse in the UK, both on and off the pitch, have highlighted the fact that there remain significant problems."
"While the general level of progress in combating racism and racist abuse in the UK is positive and should be applauded, there is much more that can and must be done, and we believe it is for the FA to take the lead and set the example for everyone, from football authorities at all levels to the grassroots groups, to follow," he added.
The report said the rise of social media and chat rooms had become a new platform for discrimination.
"We heard evidence that social media has become a tool for the spread of racist and abusive content but it is also a potential means of combating the ignorance and prejudice that lie behind such behaviour," Whittingdale said.
The report also said more needed to be done to increase the number of black and Asian coaches and officials.
Norwich City's Chris Hughton is the only black manager in the Premier League while match officials are generally white.
"There is a clear need to encourage more candidates from ethnic minorities to train as coaches and referees to ensure that clubs and boards can select from a more diverse pool of recruits from within the football pyramid," the report stated.