Mr. Red, Jude L, & Jenny the T
The terms "British Isles" & "british isles" are reserved for islands which are BRITISH. These would include the mainland of Britian, Isle of Wight, Isle of Skye, etc. but NOT the mainland of Ireland or other Irish Islands such as the Blaskett Islands, Tory Island etc.
Pretty logical really.
If you want to refer to both mainlands, and their associated smaller islands, as a group, may I suggest the term "Celtic-Anglo Archipelligo!" You never know, it might catch on!