Reports on Tuesday placed the cost of the outbreak to the FA at £100 million, and came on the day that National League side Barnet announced they had put all non-playing staff on notice of redundancy.
The Bees are unlikely to be the only club who suffer financial difficulties as a result of matches being postponed due to the virus.
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The Chancellor of the Exchequer Rishi Sunak said in a press conference on Tuesday that a £330billion package would be available as financial support to public services and businesses impacted by Covid-19, but how much of that finds its way into football remains to be seen.
Bullingham said conversations are ongoing, but that the FA’s ability to help others had also been diminished by the pandemic.
“There are some clubs particularly at the lower end of the pyramid that are going to struggle,” he said.
“I think there are many different businesses that are going to struggle over the next few weeks and months, I think we are having lots of conversations with both government and other football stakeholders about that.
“From our point of view we’re a not-for-profit (organisation); clearly the money we raise goes back into the game, we are definitely going to take a big financial hit, and we will therefore be able to put less back into the game at all levels.
“I think it will be looked at by both the Government and the football family but can’t go into any more detail on that at the moment.”
The National League announced on Monday that all three of its divisions would be suspended until early April due to the Covid-19 pandemic.
Barnet’s trip to Yeovil was among the games that did not go ahead at the weekend due to the ongoing issues and the club have now moved to cut costs.
Approximately 60 non-playing staff are being made redundant in “difficult decisions” that Bees chairman Tony Kleanthous believes were important to make sure the club “continues to survive and remains financially stable”.
“I have to be open and honest with the staff and it’s been a difficult past few days having to deliver the bad news but it’s something that had to be done,” Kleanthous said.
“I have not had time to think about plans for next season yet, but we will have to find a way to move forward based upon our current crowd attendance because existing National League rules limit any signings we can make or players’ salaries we can commit to going forward.
“The knock-on effects are of course heart-breaking for me personally as I am fully aware of how this will impact my phenomenal team of hard-working support staff across the group.”
Barnet were relegated from League Two in 2018, meaning parachute funding from the professional game for the academy will soon cease.
A club statement read: “Over the past few days, we have taken emergency measures to preserve the club and ensure it remains sustainable.
“Since relegation, we have seen a general drop in crowd attendances of 50 per cent, whilst general costs have increased resulting in operational losses of approximately £100,000 per month.
“The club budgeted for this cost in the hope of promotion but of course, at the end of April, all of our parachute funding will cease and we need to therefore make savings accordingly.
“In addition to these challenges, we have to consider the greater challenge of the impact that Covid-19 will have in the immediate and long-term future.
“In order to meet the challenges ahead of us, we will have to dismantle our existing cost structure and look to rebuild for next season with a much leaner cost base.”
Kleanthous said that head coach Darren Currie would remain in post until at least the end of the season.