Island between Iceland and Shetland, home to mouse?

Ok, my doctor got off topic, and was telling me about a British island, that is home to a mouse (both share the same name) that has survived since prehistoric times. The island itself is now controlled by the British Royal Navy as an outpost, and doesn't allow visitors. He said it's about midway between Shetland Islands and Iceland. During the Ice Age, he said it was one of three islands that didn't ice over (one of the others was the Galapagos Islands, but I can't remember the 3rd). It SOUNDED like either St. Killar or San Killar, but it was hard to understand with his accent. I've googled this to heck, and I can't find anything other than the Cyprus mouse. Thanks!