Nice idea but I think that it has been done before and this version is full of errors. Oeno and Ducie islands are both uninhabited parts of Pitcairn, which should be an answer. Montserrat and Gibraltar are both mis-spelled. "South Georgia" should be an answer without requiring the word "islands" after it. You have missed out Akrotiri and Dhekelia. Also, why are you separating Tristan da Cunha from St Helena? There's an association between both and Asencion island which you have omitted entirely. Similarly South Sandwich islands (uninhabited) are a part of South Georgia.
I'm getting my information from a Wikipedia page about the overseas territories. They don't specify if something is uninhabited. Thanks for pointing that out!