From where does Spuregon dervive his teaching authority?
The short answer is that those who have authority to preach & teach me are given that authority implicitly or explicitly by me. I give it to any preacher/teacher I listen to so long as I find their words first scriptural & then other factors come into play. I tend to select literature that was written a long time ago, literature that was written by persons who have a similar worldview as I. My worldview can be best summarized by the sovereignty of God, in all things, but especially regarding salvation. There is not a doubt in my mind, sans short lived temptations that flit through my mind due to buffeting from Satan & his helpers now & then, that God is sovereign over all. By yielding to those writers I am consistent with my worldview; my worldview matches that of scriptures; so that ultimately I am recognizing God’s authority over me. But of course God has authority over me whether I recognize it now or not.
In the instance to which you refer I have placed myself under his tutelage because I believe he speaks in accordance with the scriptures, I like his style of writing, and because I respect him as a teacher who encourages me along the Way; and his worldview can be characterized as holding to the sovereignty of God in all things.
In concluding this short answer, you also were not forced to be a member of your Church, therefore it is you who have given authority to that Church, its clergy, to preach & teach you.