Business is a busy word. It covers, not to venture outside the realm of economy, a lot of ground:
1. (a state of) economic activity, which is what you have in mind, I think,
2. ways the activity is accomplished (wheeling and dealing)
3. business set-up(s) (companies)
4. type of business (line of business, a subset of 1.)
5. must have missed something.
In sense 1
Business activity would mean "economic activity activity"
In sense 2
Business activity would mean "business wheeling and dealing" (fine)
In sense 3
Business activity would mean "companies'/company(') activity" (fine)
In sense 4
Business activity would be unclear, unless worded differently, e.g., insurance business activity, but this would again mean [insurance line-of-economic-activity] activity.