In a rare show of cross-party unity, Shadow Equalities Minister Dawn Butler said it was «the next important step to making discrimination in sport a thing of the past».
The move piles pressure on the UK Government to heed the growing calls and back the legislative tweak amid concerns about gay rights in Russia during the World Cup.
Damian Collins, the Tory chair of the Digital, Culture, Media and Sport committee, launched the drive this week in a bid to make football «a sport that is truly open to everyone».
In a report last year, his committee said fans who display homophobic attitudes at matches should face «immediate, lengthy bans», while sports authorities must adopt a «zero tolerance» approach.