I found 2. There may be more.

1
Established in 1873 at 47 1/2 Whittall Street, he moved in about 1877 to 34 Bath Street. In the early 1880s the address was 33-34 Bath Street, and in about 1886 it was 34 Bath Street only. The firm appears to have closed in about 1886.

2
Frederick William Williams established his business in 1881 at 49-50 Weaman Street, Birmingham. Between 1886 and 1890 he moved to 32-33 Weaman Street, which became known as the Birmingham Gun Works.
Between about 1913 and 1917 the name of the firm changed to Frederick Williams, and in about 1937 to Frederick Williams (Gunmakers) Ltd. Prior to adopting limited liability, the firm claimed a London address, possibly Frederick Williams of 3 Broad Street Station, Liverpool Street.

The firm closed in 1947.

Pete