At . . . . . . . . first it was difficult for her to drive . . . . . . . . car in . . . . . . . . London.

In the first blank, "first" here refers to the starting of the event, therefore "no article" will be used. "At first" is a commonly used phrase.
In the second blank, article "the" will be used because the sentence is referring to something specific (specifically the first time).
In the third blank, 'London' is a place, hence, "no article" will be used.