and many other smaller islands surrounding the islands of Great Britain and Ireland.
The term "British Isles", despite the politically suggestive use of "British", refers to these islands as a geographical--not a political--unit, although the Channel Islands are only included due to their political association. Politically, the group of islands is divided between the United Kingdom, the Republic of Ireland, the Isle of Man, the Bailiwick of Guernsey and the Bailiwick of Jersey. The last three of these are British crown dependencies, but not part of the United Kingdom.
Many people in Ireland and the Irish diaspora dislike the term "British Isles" because it may suggest incorrectly that Ireland is British. In cases where what is being referred to is the two largest islands, the term "Great Britain and Ireland" can be used. Of course, in those cases, the term "British Isles" would not be appropriate to begin with. Unfortunately there is no suitably brief term to refer to the island group as a whole; "Great Britain, Ireland, and surrounding islands" gets at the basic meaning, but at the cost of conciseness. Some writers may choose to avoid referring to the island group as a whole in order to avoid giving offense, although there are of course cases where this cannot be done while preserving the intended meaning.
In the context of the Northern Ireland peace process the term "Islands of the North Atlantic" (IONA) has been used as a neutral term to describe these islands.