Agatha Christie was a British crime writer. When she first wrote the story, the nursery rhyme she uses at the beginning was from a British nursery rhyme. When it was published in the United States, the poem was changed to include Indians, and the title was changed first to Ten Little Indians and then to And Then There Were None.
So the story actually takes place in England. On the very first page, Judge Wargrave is reading the paper and he reviews everything he has read about Soldier Island
"..... and an account of the luxurious modern house he (a millionaire American) had built on this little island off the Devon coast." (pg 1)
Soldier Island is a fictitious name based on Burgh Island off the coast of Devon. Devon is part of southwest England. Coming from this part of England, it is not unusual for the weather to suddenly turn bad and fog to roll in --- creating a trap for the visitors to the island who were unable to return to shore.