From the dissolution of partnership entries and the excellent set belonging to mycarver, the following is concrete information:
J. Drew & Son, from circa 1870/80s
156 Leadenhall Street
33 - 37 Piccadilly Circus
Kings Rd., Brighton
1882
Regents Circus, Piccadilly (plus the above addresses)
Attachment 132904
1900
Official name (as registered at Companies House) is changed to Drew & Sons (Piccadilly)
but company name of Drew & Sons is retained, too
1909
Address changes from 33-37 Piccadilly to 33, 35 & 37 Piccadilly
1928
Firm takes on Limited Company status
1973
Drew & Sons (Piccadilly) struck from Companies House Register
The name "J Drew & Son" seems to have been re-registered at some point - at least it is on file with Companies House:
Attachment 132903
Whether it is anything to do with the original company I do not know.
Regards,
Neil