When you arrive to the place where you work, you "get INTO work". INTO is the right preposition in this case.

Hi Tatyana, There is virtually no difference between "to" and "into" in this case. But you are right that "to" is the standard option. Where I live (New York State, USA), people often use "into" in place of "to" when talking about arriving at work or school or some location. Examples: - When you get into work, look up that file. - As soon as I got into school, the principal called me to his office. - I will give you a call as soon as I get into town. - What time did you get into New York? In all of these cases, the standard usage is "to", but you will hear native speakers use "into".

The wording makes it ambiguous. It could mean either: 1. He asked me "When did you [you] get in to work this morning" or 2. He asked me [a question] when I got to work this morning. Your instinct is right. "Into" would be wrong in this case. "In to" would be correct, as would just "to".