A company founded in 1826 by John Horniman, and later taken over by his son Frederick - who founded the Horniman Museum - and grandson. The company was bought out by J. Lyons & Co; the tea itself was still being sold until the 1980s.
The pub at Hay's Galleria 'Horniman at Hays' (London Bridge) commemorates the Horniman warehouse that used to be in the area.
The Wikipedia page on the Horniman Museum is [1].