Question

a fire broke out in the early hours of the morning - identify the adverbials and indicate their functions

Answer 1

Adverial:    in the early hours of the morning...

The adverbial   indicates the time of happening of the verb.. the time of the action of the verb..

Answer 2

Adverbials refers to the an adverbial phrase, adverbial clause or adverbs which provides the additional or more information about manner, place or time.  

Therefore, adverbial in the following sentence is:

1) in the early hours of the morning- It functions as adverbial of time- when something happens.