The company moved to Tottenham Court sometime between 1884 (when it was still at the 59 High Street address) and 1891 (by which time it's listed at 179 Tottenham Court in the London PO Directory). Perkins stayed at Tottenham until late 1908, when it moved to 33 Compton. There it remained for decades.
As for the Beney link, I'm a bit skeptical; I'd like to know where Pipedia (presumably your source?) got its information. What I know for sure is that by 1917 Perkins was controlled by the Adler family, and it was one of the various entities thrown into the communal pot during the merger about a decade later. I have files on this somewhere at my office and I'll see if I can find time to dig up more. I had thought Perkins remained in Cadogan, and can't think of why it alone would have been spun out.
Perkins, by the way, in addition to meerschaums and briars did silver work and made walking sticks. The business was allegedly founded in the 1850s although that sounds too early to me.
