Basil and the Lost Colony by Eve Titus, 1964.

A Norwegian scholar from the British Mousmopolitan Museum approaches Basil about a letter that he has recently received along with an arrow.  The letter mentions a recent sighting of the mysterious Adorable Snowmouse (no, that’s not a typo, he’s big for a mouse, but really adorable and saves people lost in the mountains), and the arrow is evidence that points to the whereabouts of a lost colony of mice who fled Switzerland during the time of William Tell, about 600 years previously.  These particular mice lived in William Tell’s basement, and like Tell himself, the Tellmice (as they are called) left their home because they opposed the rule of a tyrant.  However, even after the tyrant’s reign ended, the Tellmice did not return home and no one knows for sure what became of them.

Basil is eager to join the expedition to search for the lost colony, but he is also concerned about opposition from his nemesis, Professor Ratigan.  Professor Ratigan has recently made attempts on his life, and he now knows about the expedition to find the lost colony, even stealing the evidence from Basil’s home.  Basil is sure that Professor Ratigan will do everything he can to prevent them from reaching the lost colony.

In Switzerland, the expedition is joined by a pretty and adventurous opera singer, Relda (a take-off on Irene Adler, from the original Sherlock Holmes stories, read her name backwards), who comes in disguise after Basil tells her that the mission is too dangerous for her.  That’s just one of the jokes on original Sherlock Holmes stories that appear in this book.  These jokes would go over the heads of kids who aren’t familiar with the original stories, but make the story more entertaining for adults.

Basil and his friends do meet up with the Adorable Snowmouse, find the lost colony, and defeat Ratigan (well, temporarily, at least).

Although the Basil of Baker Street Series is supposed to be about a mouse detective kind of like Sherlock Holmes, some of the entries in the series, like this one, are really more adventure than mystery.  The book is currently available online through Internet Archive.