"primarily speaking" is correct and usable in written English. You can use this phrase to introduce a point which you consider to be the most important of several points. For example, "Primarily speaking, I think the most important factor in this decision is the cost.".
And when I say Bread and Puppet, I am primarily speaking of Peter Schumann, who founded the theater and continues to shape it.
"Why weren't we hearing from the churches?" Shapps was primarily speaking about the so-called bedroom tax, which comes into force on Monday and which will result in people in social housing losing 14% of their housing benefit if they are deemed to have one spare bedroom or 25% if they are deemed to have two spare rooms.
The federal term "LEP" represents a group of students primarily speaking languages other than English.
English is the primary language spoken at home, spoken by 87.2 percent, followed by Spanish at 3.3 percent, and 9.5 percent primarily speaking other languages.
(We consider ourselves international and primarily speak English).
Michael Pezzullo, secretary of the immigration department, primarily spoke for all agencies present.
(We're of Chinese heritage but we consider ourselves international and we primarily speak English).
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu