He added it was completely unacceptable that the authority had gone without a gas supplier for almost two decades, especially in light of households currently facing rising energy costs.
The comments come after Beverley Town Council received an update about the ongoing investigation into the situation at its full meeting on Monday, February 14.
He added in the meeting that the Town Council was still waiting to hear from Northern Gas Networks on how much it would have to pay to settle outstanding bills.
Councillors also heard the investigation, launched by the Personnel Committee and run by Cllr David Tucker, continues.
Northern Gas Networks is still yet to confirm whether Ofgem rules limiting back billing to no more than 12 months apply in Beverley Town Council’s case.
Coun Healy said Beverley Town Council members had resolved to right the situation, with the authority not having had a gas supplier since at least 2004.
He added that while the authority did not know the final bill, it was highly unlikely the full £35,000 set aside to cover it would be needed.
The St Marys West ward member said: “As far as the back payments go we’re in the hands of Northern Gas Networks.
“The £35,000 is unspent money the council’s been able to carry over, there’s no way I’m expecting the final bill to be anywhere near that. It was an underspend from previously and after we’ve settled this we’ll spend what’s left of it on local services and projects in the town.
“We’re not going to be doing a whip round asking the people of Beverley to pay our gas bill.
“The key question is how far back we’re going to be billed, there’s limits for domestic customers but we don’t know if they apply to businesses or councils.
“And this is at a time when people’s gas bills are going through the roof, it’s not a good situation as it is and the fact that this has been going on here is completely unacceptable.
“We’ve got our residents struggling with the cost of living at the moment, so we’ll be paying what we’re legally required to pay but only as much as is required under Ofgem rules.
“There’s also a question around which tariffs will apply, the energy price cap is set to be lifted in April so will the Town Council be charged according to the new tariffs or what we should have been paying at the time?
“The public rightly want answers about this and as elected councillors we have a responsibility to look into this and ultimately do the right thing.”