The Theatre Royal was built in 1805 in Bath, England to replace the Old Orchard Street Theatre. The building was designed by George Dance the Younger. In Persuasion, Charles invites his extended family to join him for a night a the theater: "I have been to the theatre, and secured a box for to-morrow night. A'n't I a good boy? I know you love a play; and there is room for us all" (Austen 233-234). Though he does not directly name the Theater Royal, it can be assumed that he was referring to this theater. 

"Theatre Royal" Bath." Wikipedia, https://en.wikipedia.org/wiki/Theatre_Royal,_Bath#:~:text=The%20Theatre%.... Accessed 4 December, 2022. 

Austen, Jane. Persuasion, edited by Linda Bree, Toronto, Broadview Literary Texts, 1998.