Clubs met on Friday to discuss the next steps in Project Restart with the aim to return to Premier League action in June, if the Government says it is safe to do so.
Albion are opposed to any plans to play matches at neutral venues and chief executive Barber says dialogue with Sussex Police about potential issues surrounding games behind closed doors (BCD) at the Amex are already underway.
He said: “We’ve had discussions with Sussex Police about playing behind closed doors and fans turning up. It is something they are concerned about.
“How do we stop it? I think we have to appeal to the better nature of people and the one thing I’ve been pretty impressed by is the way the British public have respected the lockdown.
“Yes of course there have been exceptions. But if you think about the population in this country and the relatively small number of incidents when lockdown has been abused, I think people have behaved impeccably.
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“I would expect Brighton fans to respect any measures we put in place to make sure a game behind closed doors took place and I’m sure my colleagues at the other 19 clubs would feel the same about their fans.
“But if we were still in a lockdown or social distancing measures were still in place, which we very much would expect them to be, and some fans simply ignored that they would obviously expect to receive punishment from the Police first and foremost. And obviously if they brought the club into disrepute then I’m sure we would look at measures as well.
“There’s always going to be someone who lets themselves down, but we can’t stop an entire industry for a relatively small amount of people who might do the wrong thing.
“Hopefully, people will continue to respect the lockdown, continue to bring the virus infections rates down and protect themselves and their families.”