A Manchester football club that has faced “appalling” alleged homophobic abuse has urged the FA to radically overhaul its disciplinary processes after further reports of discriminatory chanting.

Village Manchester FC, a team mainly comprised of gay players, formally complained to the FA after alleging players were subjected to “toxic” homophobic abuse by opponents at a match on 11 January.

In another incident at the weekend, a Championship game between Millwall and Reading was temporarily stopped following alleged homophobic chanting from a section of the home fans. Millwall said it had a zero-tolerance policy against all forms of discrimination and it would launch a “comprehensive investigation”.

The FA said it was investigating the allegations relating to a match on 11 January between Village Manchester FC and Chadderton Park Firsts, which was crowned grassroots club of the year for 2019 at an FA awards ceremony in August.

A group of Chadderton Park Firsts players allegedly chanted the words of the disco anthem YMCA at the Village Manchester players and one man was allegedly told “get up you fairy” after being injured in a tackle.

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Terry Jennings, the chairman of Chadderton, said “five idiots” had “tarnished the good name of our club” and that its first team had been suspended pending the outcome of the FA investigation.

Speaking to the Guardian on Monday, Village Manchester’s treasurer, Steve Joyce, said homophobic abuse had become much more prevalent in the grassroots game in the past two years and that players felt they could get away with it.

Joyce praised the FA’s campaign tackling discrimination in the sport but said the disciplinary measures lacked teeth. He said the system needed to be much faster with bigger fines and longer match bans for players.

“A much stronger system needs to filter down to the players who are playing every weekend and half of them don’t even realise what they’re doing is wrong, partly because the process takes so long and ends up with a slap on the wrist,” he said.

“They just carry on playing and that’s it: they don’t get the seriousness of what they’re doing, which is a criminal act.”

The FA and its county bodies aim to complete all disciplinary cases within the maximum allowance of 180 days, which it says is for exceptional cases such as those involving the police.

However, Joyce said a six-month deadline was unacceptable and that in practice it could mean the player being investigated was able to play the full season. The timescale should be cut to one month, he said, adding that the current sanctions of a small fine and a few match bans were insufficient.

An FA spokesman said: “The FA is committed to tackling homophobia, biphobia and transphobia in football at every level of the game. We will continue to work with partners across the game, such as Stonewall and LBGT fan groups, to encourage fans and players to report abuse, both at a national and county FA level, and work with the leagues, campaign groups and the statutory agencies to sanction and educate perpetrators.”