The Football Supporters’ Association has for some time backed changing the law.
Like the prime minister, it considers it to be unfair on football fans.
“I think it is outdated,” FSA chairman Tom Greatrex told the BBC Radio 4 Today programme.
“If you go to watch football in Germany or in other places around the world, then it’s perfectly acceptable.
“It is civilised and appropriate. There’s no reason why that shouldn’t be the case for football fans, as it is for fans of rugby league, watching Oasis, or anything else that happens often in the same stadiums in the same seats.”
The FSA’s position is that clubs should have the choice, in consultation with supporters, to sell alcohol.
Clubs might want to offer it in all stands, others in designated areas, while a few might choose not to do so at all.
Other sports offer designated alcohol-free sections, something that football clubs may wish to copy for some families and supporters who do not consume alcohol because of their religion.
The FSA acknowledges this, but believes having the option to make such decisions is important.
It believes relaxing the law would be more popular the further down the leagues you go, where alcohol sales could potentially provide a crucial additional income stream.
The UK Football Policing Unit rejected the suggestion, arguing alcohol plays “a significant part in violent and disorderly behaviour” and that “other sports simply don’t see the violence and criminal behaviour” that football does.
Yet for Greatrex, there is already proof police are not open to ideas through their previous opposition to safe standing.
Before it was introduced four years ago, Mark Roberts, who has been the national lead for football policing since 2014, told the BBC it would make it “easier to throw missiles, engage in hate chanting, racism, sneak alcohol in, take cocaine”.
“[The police] were telling everybody that we couldn’t have standing at football again, that it would jeopardise safety, ” Greatrex said.
“Actually, what we saw then was a controlled, managed pilot projects to get that re-established.
“There hasn’t been the level of disorder that some of the police sources were saying there would be. I think the police should have more of an open mind and engage in this in a sensible and mature way.”