into has a lot of meanings. I normally use it when I mean to go inside:
into: to the inside or middle of a place, container, area, etc.
Let's go into the garden. Cambridge Dictionary
I saw the following example on one of Oxford conversation videos
I don't fancy of driving back tonight. Why don't we stay near here then we can go straight into work tomorrow.
We don't go inside the work, we go to the work.
So, Is it common to use into with work?
Best Answer
Yes, it's fine. I couldn't tell you when you might use over the other, since it's mostly a matter of context and preference.
Using "into" slightly emphasizes the image of being forced to go and do something you'd rather not do, like someone is forcing you into a small, uncomfortable room:
Although, perhaps that just my personal experience. I could use "to" in the same sentence without changing the meaning:
As others have pointed out, the use of "into" for this is relatively recent (since 1990). Many feel it should be two words, "go in to work" since "into" should refer to the action of going inside something. But evolving English means that "into" is common.