Ministers were criticised earlier this year for making it "difficult" for authorities to get answers over how to mitigate any impact of leaving the EU.
The government has said it does not expect any supply shortages after Brexit, but the state is actively discouraging people from stockpiling goods to avoid problems.
Now it's been suggested that authorities were denied information to stop panic buying, which would create a shortage in itself.
Wakefield Council has set aside £5m in reserves for any sudden changes that might take effect as a result of Brexit, but says if the UK leaves with a deal "nothing will change", and the cash is unlikely to be needed.
Speaking at a meeting of scrutiny committee chairpeople on Monday, Vince Macklam, from the council's emergency planning department said: "The government was restricting the amount of information that went out to local authorities, and by extension the wider public, because they were worried about the impact of food or fuel shortages.
"From a planning point of view, we've done everything we need to do.
"At present, central government doesn't think there will be a shortage of food, so we're not worried about that.
"On the other key issue, which is around fuel and utility supplies, the government's risk assessment says they're not anticipating any issues.
"Most of our fuel supply comes from outside the EU anyway."
The council's chief legal officer, Gillian Marshall, said that the government had taken control of the whole preparation process to stop discrepancies between individual areas.
She said: "We've been asked not to put out our own communication messages on Brexit because of a lot of things have been done centrally to avoid whole regions doing their own thing.
"The government thought it would create a situation where people were really frightened about what might happen.
"We've not always had the flow down of information we would have liked, but at least by giving the government our information, we can be assured they've got the best possible view of what's going on locally.
"The message is, don't stockpile food, fuel and medication.
"If there's a deal, nothing will change."
Local Democracy Reporting Service