Berkeley Galleries is where Mr. Sidney Darrell's work was displayed in, The Romance of a Shop and it is located on New Bond Street. In the 19th century Bond Street became less known as a social area and more of a place for luxury shoppings. Galleries opened on Bond Street around the time of the novel, and today Bond Street has maintained its reputation for high end shopping and fashion, sometimes being known as the best retail location in all of Europe.
''We understand that the exhibition of Mr. Sidney Darrell, A.R.A.'s pictures, to be held in the Berkeley Galleries, New Bond Street, will be opened to the public on the first of next month"
"At luncheon, Phyllis reminded her that to-night was the night of Mr. Darrell's conversazione at the Berkeley Galleries, for which he had sent them two tickets"
http://www.wickedwilliam.com/tag/bond-street/
https://www.loc.gov/item/2001695082/
https://www.alamy.com/people-shopping-in-new-bond-street-london-uk-image156952681.html