In Chapter XXXVI, with great seriousness Wemmick tells Pip,
“Walworth is one place, and this office is another. Much as the Aged is one person, and Mr. Jaggers is another. They must not be confounded together. My Walworth sentiments must be taken at Walworth; none but my official sentiments can be taken in this office.”
Thus, it is that Wemmick has a facade for work that he dispenses with at his home, Walworth. While he is clerk for Mr. Jaggers in Little Britain, Wemmick is stoic, with a "post office mouth" that seems mechanical in his chiseled face that has "...glittering eyes—small, keen, and black." For all appearances, Wemmick is an unfeeling person, who simply goes about the duties of his business position.
However, when Pip accompanies Wemmick to his home outside London, a home to which Wemmick has attached the appellation of Walworth, the little dry man with a wooden face becomes very human. The little cottage has a lovely garden; oddly, though, there is a flagstaff and a little bridge, near which is a cannon. In the back, Wemmick has a pig and fowls and rabbits and a garden. As Pip gazes at it all, Wemmick tells Pip that his home is a good thing to brush away the "Newgate cobwebs away, and pleases the Aged," his father.
Further, Wemmick is a warm, loving son to his deaf father. He prepares a delicious supper for Pip and his parent, and puts Pip in a comfortable little room shaped like a turret. But, when back at the office, Wemmick is his little wooden self again.