A report in The Sun said the Devizes Lions May Fayre had fallen foul of council demands for an anti-terror plan.
But Lions president Roger Stratton blamed bureaucracy for the decision.
He also added he had "never witnessed" parsnip wine-induced drunkenness among visitors, despite the report's claims.
The annual event on the May Day bank holiday attracts hundreds of visitors to the Wiltshire town centre.
Wiltshire Council was reported by the newspaper as wanting the town square security strengthened after last month's attack in Westminster.
Mr Stratton told the BBC the cancellation was caused by council red tape, not "far-fetched" fears about terrorism.
"The problem is for many years we have filled in an event-management plan and this year we had an email back from the council running to three pages asking for more information about 'this and that'," he said.
"For example, we have a trailer promoting local bands during the afternoon and we were asked how we would monitor the noise, to which my last response was 'I have an ear on one side and an ear on the other'."
The Sun's article also added the only trouble in the fair's 20-plus year history had been "drinkers quaffing too much parsnip wine".
Mr Stratton insisted: "I don't think there has been one case of drunkenness, as I far as I can recall."
A Wiltshire Council spokesman said the Lions' plan "couldn't guarantee a safe event" but "would be happy to work with the club to help them plan the event in good time for future years".
The organisers of a May Day bank holiday fair have rubbished newspaper reports they cancelled this year's event due to terrorism fears.