The islands, which have recorded no Covid cases since September, remain under the most lenient restrictions which allow up to six people to meet indoors – including in pubs and restaurants.
All other parts of the country are either in tier 3 or 4, with more than three-quarters of the population effectively ordered to ‘stay at home’.
It comes after police refused entry to five people who had flown in on Christmas Eve after they apparently broke Covid travel restrictions.
“We strongly urge anyone planning to travel to the islands to reconsider, in light of what bringing the virus to the islands could mean for our community, particularly at this time of year,” the Council of the Isles of Scilly said in a statement.
Linda Thomas, a 69-year-old librarian from St Mary’s, said residents were worried about the risk of the virus spreading to the isles, which have only one small hospital and an ageing population.
“Having seen our family and friends in Cornwall go from a Tier 1 to a Tier 3 in under a week because of mindless selfish people from higher tiers travelling down is very disturbing,” Ms Thomas said.
“We know that some of these people were heading to the islands and I have no doubt that some made it.”
Another islander, Barbara Simpson, 78, said: “Those who freely admit they have come to Scilly to get away from the virus obviously have no idea or don’t care, of the risk they pose to us.
“The total lack of awareness and arrogance of these people is staggering.”
Jonathan Smith, a councillor for St Martin’s who also runs a small organic fruit and vegetable farm, said that Scilly being the only place left in tier 1 was an “interesting paradox”.
“We are probably the place in the country for fewest options for travel, shopping and eating out in the winter months,” he said.
Mr Smith also stressed that outsiders should not travel to the islands for a “New Year or winter holiday”.
The 2,000 residents of the Isles have been advised to stay local for their New Year’s Eve celebrations.
“Please consider whether the risk of spreading the virus on a single night out is worth jeopardising the massive effort made to keep our community and services safe so far this year,” said the Council of the Isles of Scilly.
“As we have previously advised, just because you can do something, doesn’t necessarily mean you should, so please consider the prime minister’s advice to ‘see in the new year safely at home.’
Several residents said they were staying home for the celebrations, but Tim Jones, who moved to St Mary’s from London six years ago, said he and his partner would be wearing fancy dress to visit his local pub in Old Town.
“We are making the most of it for the children, but finish by 7pm,” said the 55-year-old IT consultant.
Additional reporting by Press Association