Sergeant Bob MacKay, the senior officer in Arran’s tiny police force, wears a weary smile as he presses his peaked cap carefully on to his head. “You cannot tilt this hat aggressively,” he says. “It has a non-tilt mechanism.”

If there is an air of resignation about Sergeant MacKay, it is understandable. A week ago, under the headline “Police accused of not smiling enough”, he and his squad of four officers were lambasted in the Arran Banner by the chairman of the island’s community council, Campbell Laing. Prominent among Mr Laing’s charges was the “aggressive way” the officers were wearing their hats.

At a meeting of the community council last month Mr Laing, a former detective himself, suggested that there was a problem with the officers’ attitude. “People are telling me that the hostile nature of the police and their finger-pointing attitude is unwelcome. You know what my background is and I do not think this aggressive style of policing is justified. How hard would it be for officers to smile?”

Allegations of authoritarianism seem incongruous. True, Sergeant MacKay and his colleagues come equipped with all the disturbing accoutrements of modern policing: body armour, CS gas, walkie-talkies, batons and handcuffs. But this is Arran, population 5,000. The island, 167 square miles of mountains and glens marooned an hour from the Ayrshire coast, is marketed as “Scotland in miniature”, a place where sheep-worrying is a concern.

Sergeant MacKay’s attitude to his baton speaks volumes for the distinctiveness of island policing: “It’s useful if an old lady’s fallen down in her house and you’ve got to break a window to get in.”

So why doesn’t he simply dismiss the allegations of aggression, or say something rude about the people who accuse him? “It’s not in me,” he says. “I’ve been here ten years and that’s not how it works. Confidentiality is the key on the island. Confidentiality looks after everyone. You’ve got to build trust.”

It is, however, this same issue of trust that fires up his most strident critic. Mr Laing retired to the island 17 years ago. These days he wears a kilt in the Graham tartan, and works as a tour guide in the Arran Distillery.

His argument is not about hats but about “the demeanour and attitude” of the police, about people being stopped for speeding when travelling at 32mph on the way to a funeral, or finding themselves being questioned in the back of a police van for failing to wear a safety belt.

“It’s something foreign in a small community,” he says. “It’s a question of demeanour. I see a change, an attitude change in how the police deal with the public.”

According Ian Small, one of Mr Laing’s supporters, Arran was in danger of becoming a police state. “I have lived here all my life and I’ve never known it so bad — it’s like they have quotas to fill,” says Mr Small, 54, an electrician. The worst incident, he says, occurred earlier this summer when the police set out to breathalyse every driver coming off the ferry from Ardrossan.

“They said they had received a tip-off that there had been drinking in the bar. What was the result? Queues forever, and bad feeling. Welcome to Arran.”

Sergeant MacKay says that there are no quotas and that the policy on drink driving was aimed at curbing fatal road accidents — there have been seven deaths in the past eight years — and was supported by the Arran Alcohol Forum, a impressive local alliance of health and education services.

If Sergeant MacKay is too canny to attack his critics in the press, there is little doubt that he went along to last month’s community council determined to lance this boil of criticism. Irked by the minutes of July’s meeting in which “Campbell Laing expressed concern that aggressive policing was sapping public confidence”, Sergeant MacKay’s opening gambit was to pull out a picture of the Jack Warner, the actor who played Dixon of Dock Green, the friendliest of television bobbies, and suggest: “This is what you think we’re like.”

One observer, who asked not be named, wondered whether this bold move “could have gone horribly wrong for Bob”. Instead, Mr Laing’s explosion of anger “turned things into a farce”, made the headlines and set tongues wagging in every bar from Lamlash to Lochranza.

The letters page of the Arran Banner has been filled with indignant responses to Mr Laing’s remarks. “I could not care less how they were their hats as long as they carry out their duties properly,” wrote Lady Jean Fforde, adding that the Arran police were a “great advertisement for the youth of today”. Tom Sheldon, of Lamlash described Mr Laing’s comments as “fatuous nonsense” while Brenda Stewart, a community councillor, wrote: “We are fortunate to have Bob MacKay.”

This public demonstration of support for the police may not be the end of the matter. Mr Small is something of a local legend for his campaigning and Mr Laing is no less of a fighter. Outnumbered on the community council, and derided by the letter writers, he intends to take his case to a higher power and write to a chief inspector of Strathclyde Police to air his grievance.

Sergeant MacKay is too polite to comment. He shakes his head, and from beneath the chequered band of his hat he says: “Everyone is entitled to an opinion. If he represents a section of the community, I’ll take what he says on board. If not . . . ”

And with a shrug, it’s back to the sheep worriers.

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