As Sergeant Colin Taylor strolls down the high street in uniform, almost everyone he passes greets him by name. He exchanges observations about the weather; drivers wave from their cars, pointing at their seatbelts to show they're wearing them; the occasional tourist asks for directions.

This archetypal British image of a bobby on the beat isn't a nostalgic recollection from decades past, nor a fictional detective to take the baton from Hamish Macbeth or Dixon of Dock Green. This is real life on the Isles of Scilly, the sub-tropical islands that lie 28 miles west of Cornwall, where community policing is going strong and a total of five crimes have been reported so far this year. It's also where one of the two cells in the police station is currently being used to store a Christmas tree, as so far it has not been needed for criminals.

Sergeant Taylor's work has a growing worldwide following thanks to the fact that he chronicles incidents on the Isles of Scilly Police Facebook page, under the tagline "Like Heartbeat, but less frenetic". His recent advertisement for a new police officer to replace PC Faye Webb, who returned to Plymouth last week, included key skills such as, "Unflinching confidence to know what to do when you are alerted to an abandoned seal pup making its way up the main street" and "An acceptance that at 6.15pm you will be handed an item of lost property while off duty in the Co-op queuing for the till with both arms laden." It attracted lighthearted applications from around the world, many professing strong cookery skills and a desire to make cake for Taylor. He is currently interviewing applicants from Devon & Cornwall Police for the role.

Sergeant Colin Taylor and his usual transport, the police Land Rover (Genevieve Roberts)

"We've returned to uniform to be here," Taylor says of himself and his colleague Mat Crowe, who work with police community support officer Shirley Graham to police the islands, staggering their shifts so there is always someone on duty until they've "put the town to bed", though officers are on call 24 hours a day. "We're detectives, traffic, licensing, shotguns, youth intervention, everything." In June last year, the team stood in to help a couple getting married, witnessing their nuptials and acting as photographer. Their services have already been requested for another ceremony this summer. I join them on patrol to check that there's no dangerous, or just plain silly, driving on Scilly, Taylor exchanging waves with every vehicle we pass.

"If you're approachable, people will talk to you, and that approachableness is 24 hours a day. People do come to us and let us know what is going on," he says. "We're not judges – we don't want to humiliate people." People have sent cards to the officers after being in custody, thanking them for making an unpleasant experience less painful. Of the 7.5 million offences committed in the UK last year, 57 took place on Scilly, where some 2,200 people live on St Mary's and the "off islands" of St Martin's, St Agnes, Bryher and Tresco.

A few weeks ago, Taylor posted an apology for disturbing the peace, when an "ever so keen" officer over from Truro tested the sirens on the police Land Rover, which are never heard on Scilly. "We can progress through traffic fast enough already," he explains. "So it seems a bit dramatic and rude. If we put them on, people start behaving like cats and change direction. Also, I may be going to something sensitive, life-changing or humiliating. I don't want to highlight that – it's not like there's the anonymity of the mainland."

On the "off islands", the speediest way to get to a job can involve jumping on the bucket container on the back of a tractor, or hitching a lift on a golf buggy. Last year, Colin got wind that driving-under-the-influence was happening on Bryher. "The only way to get close to the island was to get a boat to Tresco. So I took the tourist boat, and was chatting to a family with an 11-year-old boy, Isaac. I said I needed to get to the other side of the island, and he offered me his push-bike. Tourists evidently couldn't believe their eyes: I was in full uniform, helmet, knees going up around my ears as I rode." A local boatman on the other side of the island whisked him over to Bryher, just in time for him to make the arrest. Another boat brought him and his prisoner back to St Mary's. "It was one of the best day's work I've ever had. Everything was unplanned but went like clockwork. "

We pass by the secondary school, where pupils from all the islands study until the age of 16, and where police deliver a sizeable part of the citizenship element on the curriculum. Ofsted has praised their work, which involves "999 week" for year nines. "We introduce them to policing, courts, first aid. Then, in year 10, they are taken to the mainland for a week," Taylor says.

He explains that the team focus on problems as they are developing and catching them before they descend into crime. This doesn't make the islands immune to serious crime. Two years ago, a yacht sailed in, and when the border force came onboard the solo yachtsman climbed the mast and plunged to his death on the quay below. There was £20m worth of cocaine onboard. The last murder took place in 1975, when a father murdered his son. It was a dark time in Scilly history. "We work very closely with social services, looking out for vulnerable people."

But with such a low rate of arrest, I can't help wondering if the police ever wish for some really juicy crime to get stuck into. PC Faye Webb explains that this is not the case. "It's very personal policing," she says. "If there is a crime we probably know the victims, so there is emotion attached."