A coalition government was in . . . . . . . . power in Britain during . . . . . . . . Second World War.

Option C is correct because the first blank doesn't require articles to provide meaning to the sentence. 'In a power' is meaningless here. 'The' is used in the second blank to provide sense to the sentence. 'The' refers to a particular time & shows the uniqueness of the subject of which the readers are aware of.