Yes, there is a very small colony on a small uninhabited chain of tiny islands called the Shiant Isles. One of the rarest mammals in the UK, the Western Isles population is confined to the Shiants because there are no brown rats present and the black rat enjoys a plentiful supply of food along the shoreline and amongst the seabird population.
The brown rat, which did not reach the Western Isles until the 18th Century, has replaced the black rat elsewhere in the Western Isles. It’s generally thought that the first brown rats to make landfall came ashore from the wreckage of the King of Prussia, a sailing ship which ran aground off the Isle of Lewis in 1768.
Black rats have something of a bad reputation despite their relatively scarcity as they can carry a host of nasty diseases including bubonic plague, typhus and rabies.
In the Western Isles, black rats wiped out the population of North Rona in 1685 after coming ashore from a ship wreck. Whether the death toll was due to bubonic plague or the rats eating the islanders out of house and home is not recorded.