Whether it is into or in to depends upon the meaning and part of speech of the word work. If work means the action of doing the job and is therefore a verbal, it is two words, in to. If work is a physical location and is therefore a noun, it is one word, into.
And I don’t think you can always tell the difference in the meaning.
…I went in to work. (the action of doing the job)
…I went into work. (the physical location)