"actually speaking" is correct and usable in written English. You can use it when you want to emphasize something that you are saying or when you want to introduce a different perspective or a counter-argument. For example, "Actually speaking, I don't think that's the best way to go about solving the problem."
Kramer told the Guardian: "I am supporting Bernie because he's the only candidate that's actually speaking to the actual challenges that the country faces".
This choice was made to convey their personalities without them actually speaking, as Rare believed the actual speech "could ruin the player's perception of the characters".
"There's this annoyance that she's actually speaking up for herself.
"Vic, Vic," I said, so drunk I was unsure I was actually speaking.
It's the fact that you are actually speaking about what people do, that excites you?
Are we actually speaking to each other or just passing by?
I remember the amazement I felt that a real New Yorker was actually speaking to me.
In the Guardian US office, the record of Snowden actually speaking was cathartic.
"I felt like we'd said a lot to each other but without actually speaking".
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia