My aunt lived on . . . . . . . . ground floor of . . . . . . . . old house on . . . . . . . . River Thames.

In the first blank, article "the" will be used because article 'the' is used to refer to something specific. Here 'ground floor' is a specific entity.
In the second blank, article "an" will be used because old house is a common noun, something general. It has a vowel sound, hence, 'an' is used.
In the third blank, 'River Thames' is a proper noun, hence, article "the" will be used.